当前期刊: Random Structures & Algorithms Go to current issue    加入关注   
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • Ramsey games near the critical threshold
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-17
    David Conlon; Shagnik Das; Joonkyung Lee; Tamás Mészáros

    A well‐known result of Rödl and Ruciński states that for any graph H there exists a constant C such that if , then the random graph Gn, p is a.a.s. H‐Ramsey, that is, any 2‐coloring of its edges contains a monochromatic copy of H. Aside from a few simple exceptions, the corresponding 0‐statement also holds, that is, there exists c > 0 such that whenever the random graph Gn, p is a.a.s. not H‐Ramsey

    更新日期:2020-10-17
  • Long paths and connectivity in 1‐independent random graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-16
    A. Nicholas Day; Victor Falgas‐Ravry; Robert Hancock

    A probability measure on the subsets of the edge set of a graph G is a 1‐independent probability measure (1‐ipm) on G if events determined by edge sets that are at graph distance at least 1 apart in G are independent. Given a 1‐ipm , denote by the associated random graph model. Let denote the collection of 1‐ipms on G for which each edge is included in with probability at least p. For , Balister and

    更新日期:2020-10-17
  • Hamilton cycles in random graphs with minimum degree at least 3: An improved analysis
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-16
    Michael Anastos; Alan Frieze

    In this paper we consider the existence of Hamilton cycles in the random graph . This random graph is chosen uniformly from , the set of graphs with vertex set [n], m edges and minimum degree at least 3. Our ultimate goal is to prove that if m = cn and c > 3/2 is constant then G is Hamiltonian w.h.p. In Frieze (2014), the second author showed that c ≥ 10 is sufficient for this and in this paper we

    更新日期:2020-10-17
  • A probabilistic approach to the leader problem in random graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-15
    Louigi Addario‐Berry; Shankar Bhamidi; Sanchayan Sen

    We study the fixation time of the identity of the leader, that is, the most massive component, in the general setting of Aldous's multiplicative coalescent, which in an asymptotic sense describes the evolution of the component sizes of a wide array of near‐critical coalescent processes, including the classical Erdős‐Rényi process. We show tightness of the fixation time in the “Brownian” regime, explicitly

    更新日期:2020-10-17
  • Vertex Ramsey properties of randomly perturbed graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-14
    Shagnik Das; Patrick Morris; Andrew Treglown

    Given graphs F, H and G, we say that G is (F, H )v‐Ramsey if every red/blue vertex coloring of G contains a red copy of F or a blue copy of H. Results of Łuczak, Ruciński and Voigt, and Kreuter determine the threshold for the property that the random graph G(n, p) is (F, H )v‐Ramsey. In this paper we consider the sister problem in the setting of randomly perturbed graphs. In particular, we determine

    更新日期:2020-10-14
  • Resolution of a conjecture on majority dynamics: Rapid stabilization in dense random graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-13
    Nikolaos Fountoulakis; Mihyun Kang; Tamás Makai

    We study majority dynamics on the binomial random graph G(n, p) with p = d/n and , for some large . In this process, each vertex has a state in {− 1, + 1} and at each round every vertex adopts the state of the majority of its neighbors, retaining its state in the case of a tie. We show that with high probability the process reaches unanimity in at most four rounds. This confirms a conjecture of Benjamini

    更新日期:2020-10-13
  • Successive shortest paths in complete graphs with random edge weights
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-13
    Stefanie Gerke; Balázs F. Mezei; Gregory B. Sorkin

    Consider a complete graph Kn with edge weights drawn independently from a uniform distribution U(0, 1). The weight of the shortest (minimum‐weight) path P1 between two given vertices is known to be , asymptotically. Define a second‐shortest path P2 to be the shortest path edge‐disjoint from P1, and consider more generally the shortest path Pk edge‐disjoint from all earlier paths. We show that the cost

    更新日期:2020-10-13
  • The Kőnig graph process
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-09
    Nina Kamčev; Michael Krivelevich; Natasha Morrison; Benny Sudakov

    Say that a graph G has property if the size of its maximum matching is equal to the order of a minimal vertex cover. We study the following process. Set and let e1, e2, … eN be a uniformly random ordering of the edges of Kn, with n an even integer. Let G0 be the empty graph on n vertices. For m ≥ 0, Gm + 1 is obtained from Gm by adding the edge em + 1 exactly if Gm ∪ {em + 1} has property . We analyze

    更新日期:2020-10-11
  • Fast algorithms at low temperatures via Markov chains
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-05
    Zongchen Chen; Andreas Galanis; Leslie A. Goldberg; Will Perkins; James Stewart; Eric Vigoda

    Efficient algorithms for approximate counting and sampling in spin systems typically apply in the so‐called high‐temperature regime, where the interaction between neighboring spins is “weak.” Instead, recent work of Jenssen, Keevash, and Perkins yields polynomial‐time algorithms in the low‐temperature regime on bounded‐degree (bipartite) expander graphs using polymer models and the cluster expansion

    更新日期:2020-10-05
  • Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-10-03
    Jean‐François Delmas; Jean‐Stéphane Dhersin; Marion Sciauveau

    We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. This result is a first step for giving a nonparametric test for identifying the degree function of a large random graph. Replacing the indicator function in the empirical CDF by a smoother function

    更新日期:2020-10-04
  • Local limit theorems for occupancy models
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-09-27
    A. D. Barbour; Peter Braunsteins; Nathan Ross

    We present a rather general method for proving local limit theorems, with a good rate of convergence, for sums of dependent random variables. The method is applicable when a Stein coupling can be exhibited. Our approach involves both Stein's method for distributional approximation and Stein's method for concentration. As applications, we prove local central limit theorems with rate of convergence for

    更新日期:2020-09-28
  • Partial resampling to approximate covering integer programs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-09-27
    Antares Chen; David G. Harris; Aravind Srinivasan

    We consider column‐sparse covering integer programs, a generalization of set cover. We develop a new rounding scheme based on the partial resampling variant of the Lovász Local Lemma developed by Harris and Srinivasan. This achieves an approximation ratio of , where amin is the minimum covering constraint and is the maximum ℓ1‐norm of any column of the covering matrix A (whose entries are scaled to

    更新日期:2020-09-28
  • Very fast construction of bounded‐degree spanning graphs via the semi‐random graph process
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-09-27
    Omri Ben‐Eliezer; Lior Gishboliner; Dan Hefetz; Michael Krivelevich

    In this paper, we study the following recently proposed semi‐random graph process: starting with an empty graph on n vertices, the process proceeds in rounds, where in each round we are given a uniformly random vertex v, and must immediately (in an online manner) add to our graph an edge incident with v. The end goal is to make the constructed graph satisfy some predetermined monotone graph property

    更新日期:2020-09-28
  • Asymptotic normality of the number of corners in tableaux associated with the partially asymmetric simple exclusion process
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-09-27
    Paweł Hitczenko; Aleksandr Yaroslavskiy

    In this paper, we study corners in tree‐like and permutation tableaux. Tree‐like tableaux are in bijection with other combinatorial structures, including permutation tableaux, and have a connection to the partially asymmetric simple exclusion process (PASEP), an important model of an interacting particles system. In particular, in the context of tree‐like tableaux, a corner corresponds to a node occupied

    更新日期:2020-09-28
  • The Glauber dynamics for edge‐colorings of trees
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-09-26
    Michelle Delcourt; Marc Heinrich; Guillem Perarnau

    Let T be a tree on n vertices and with maximum degree . We show that for the Glauber dynamics for k‐edge‐ colorings of T mixes in polynomial time in n. The bound on the number of colors is best possible as the chain is not even ergodic for . Our proof uses a recursive decomposition of the tree into subtrees; we bound the relaxation time of the original tree in terms of the relaxation time of its subtrees

    更新日期:2020-09-26
  • On edge‐ordered Ramsey numbers
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-09-02
    Jacob Fox; Ray Li

    An edge‐ordered graph is a graph with a linear ordering of its edges. Two edge‐ordered graphs are equivalent if there is an isomorphism between them preserving the edge‐ordering. The edge‐ordered Ramsey number redge(H; q) of an edge‐ordered graph H is the smallest N such that there exists an edge‐ordered graph G on N vertices such that, for every q‐coloring of the edges of G, there is a monochromatic

    更新日期:2020-09-02
  • Short proofs of some extremal results III
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-08-30
    David Conlon; Jacob Fox; Benny Sudakov

    We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short.

    更新日期:2020-08-31
  • Characterization of quasirandom permutations by a pattern sum
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-08-27
    Timothy F. N. Chan; Daniel Král'; Jonathan A. Noel; Yanitsa Pehova; Maryam Sharifzadeh; Jan Volec

    It is known that a sequence of permutations is quasirandom if and only if the pattern density of every 4‐point permutation in converges to 1/24. We show that there is a set S of 4‐point permutations such that the sum of the pattern densities of the permutations from S in the permutations converges to if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the sets

    更新日期:2020-08-28
  • On‐line balancing of random inputs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-08-25
    Nikhil Bansal; Joel H. Spencer

    We consider an online vector balancing game where vectors vt, chosen uniformly at random in {− 1, + 1}n, arrive over time and a sign xt ∈ {− 1, + 1} must be picked immediately upon the arrival of vt. The goal is to minimize the L∞ norm of the signed sum . We give an online strategy for picking the signs xt that has value O(n1/2) with high probability. Up to constants, this is the best possible even

    更新日期:2020-08-25
  • Embedding spanning subgraphs in uniformly dense and inseparable graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-08-24
    Oliver Ebsen; Giulia S. Maesaka; Christian Reiher; Mathias Schacht; Bjarne Schülke

    We consider sufficient conditions for the existence of kth powers of Hamiltonian cycles in n‐vertex graphs G with minimum degree for arbitrarily small . About 20 years ago Komlós, Sarközy, and Szemerédi resolved the conjectures of Pósa and Seymour and obtained optimal minimum degree conditions for this problem by showing that suffices for large n. For smaller values of the given graph G must satisfy

    更新日期:2020-08-25
  • Ronald Louis Graham (1935 ‐ 2020)
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-08-16

    Figure 1 Open in figure viewerPowerPoint

    更新日期:2020-08-24
  • Seeded graph matching via large neighborhood statistics
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-30
    Elchanan Mossel; Jiaming Xu

    We study a noisy graph isomorphism problem, where the goal is to perfectly recover the vertex correspondence between two edge‐correlated graphs, with an initial seed set of correctly matched vertex pairs revealed as side information. We show that it is possible to achieve the information‐theoretic limit of graph sparsity in time polynomial in the number of vertices n. Moreover, we show the number of

    更新日期:2020-08-17
  • Rapid mixing of the switch Markov chain for strongly stable degree sequences
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-07-20
    Georgios Amanatidis; Pieter Kleer

    The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show that the switch chain for sampling simple undirected graphs with a given degree sequence is rapidly mixing when the degree sequence is so‐called strongly stable. Strong stability is satisfied by all degree sequences for which the switch

    更新日期:2020-08-17
  • Local decoding and testing of polynomials over grids
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-27
    Mitali Bafna; Srikanth Srinivasan; Madhu Sudan

    We study the local decodability and (tolerant) local testability of low‐degree n‐variate polynomials over arbitrary fields, evaluated over the domain {0,1}n. We show that for every field there is a tolerant local test whose query complexity depends only on the degree. In contrast we show that decodability is possible over fields of positive characteristic, but not over the reals.

    更新日期:2020-08-17
  • On the discrepancy of random low degree set systems
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-13
    Nikhil Bansal; Raghu Meka

    Motivated by the celebrated Beck‐Fiala conjecture, we consider the random setting where there are n elements and m sets and each element lies in t randomly chosen sets. In this setting, Ezra and Lovett showed an discrepancy bound when n ≤ m and an O(1) bound when n ≫ mt. In this paper, we give a tight bound for the entire range of n and m, under a mild assumption that . The result is based on two steps

    更新日期:2020-08-17
  • Coloring triangle‐free graphs with local list sizes
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-07-13
    Ewan Davies; Rémi de Joannis de Verclos; Ross J. Kang; François Pirot

    We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of triangle‐free graphs. In both our results, we permit the amount of color made available to vertices of lower degree to be accordingly lower. One result concerns list coloring and correspondence coloring, while the other concerns fractional coloring

    更新日期:2020-08-17
  • Weighted distances in scale‐free preferential attachment models
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-07-03
    Joost Jorritsma; Júlia Komjáthy

    We study three preferential attachment models where the parameters are such that the asymptotic degree distribution has infinite variance. Every edge is equipped with a nonnegative i.i.d. weight. We study the weighted distance between two vertices chosen uniformly at random, the typical weighted distance, and the number of edges on this path, the typical hopcount. We prove that there are precisely

    更新日期:2020-08-17
  • Existence thresholds and Ramsey properties of random posets
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-08-06
    Victor Falgas‐Ravry; Klas Markström; Andrew Treglown; Yi Zhao

    Let denote the power set of [n ], ordered by inclusion, and let denote the random poset obtained from by retaining each element from independently at random with probability p and discarding it otherwise. Given any fixed poset F we determine the threshold for the property that contains F as an induced subposet. We also asymptotically determine the number of copies of a fixed poset F in . Finally, we

    更新日期:2020-08-06
  • 1‐Factorizations of pseudorandom graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-21
    Asaf Ferber; Vishesh Jain

    A 1‐factorization of a graph G is a collection of edge‐disjoint perfect matchings whose union is E (G ). In this paper, we prove that for any ϵ >0, an (n ,d ,λ )‐graph G admits a 1‐factorization provided that n is even, C 0 ≤ d  ≤ n −1 (where C 0=C 0(ϵ ) is a constant depending only on ϵ ), and λ  ≤ d 1−ϵ . In particular, since (as is well known) a typical random d ‐regular graph G n ,d is such a graph

    更新日期:2020-07-21
  • The real tau‐conjecture is true on average
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-15
    Irénée Briquel; Peter Bürgisser

    Koiran's real τ ‐conjecture claims that the number of real zeros of a structured polynomial given as a sum of m products of k real sparse polynomials, each with at most t monomials, is bounded by a polynomial in mkt . This conjecture has a major consequence in complexity theory since it would lead to superpolynomial lower bounds for the arithmetic circuit size of the permanent. We confirm the conjecture

    更新日期:2020-07-21
  • A simple network of nodes moving on the circle
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-01
    Dimitris Cheliotis; Ioannis Kontoyiannis; Michail Loulakis; Stavros Toumpis

    Two simple Markov processes are examined, one in discrete and one in continuous time, arising from idealized versions of a transmission protocol for mobile networks. We consider two independent walkers moving with constant speed on the discrete or continuous circle, and changing directions at independent geometric (respectively, exponential) times. One of the walkers carries a message that wishes to

    更新日期:2020-07-21
  • Ramsey, Paper, Scissors
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-07-20
    Jacob Fox; Xiaoyu He; Yuval Wigderson

    We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on n vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when

    更新日期:2020-07-20
  • Sharp bounds for the variance of linear statistics on random permutations
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-07-20
    Eugenijus Manstavičius

    We are concerned with the variance of a completely additive function defined on the symmetric group endowed with the Ewens probability. Overcoming specific dependence of the summands, we obtain the upper and lower bounds including optimal constants. We also derive a decomposition of such a function into a sum with uncorrelated summands. The results can be reformulated for the linear statistics defined

    更新日期:2020-07-20
  • The range of once‐reinforced random walk in one dimension
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-07-10
    Peter Pfaffelhuber; Jakob Stiefel

    We study once‐reinforced random walk on . For this model, we derive limit results on all moments of its range using Tauberian theory.

    更新日期:2020-07-10
  • Site percolation and isoperimetric inequalities for plane graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-25
    John Haslegrave; Christoforos Panagiotis

    We use isoperimetric inequalities combined with a new technique to prove upper bounds for the site percolation threshold of plane graphs with given minimum degree conditions. In the process we prove tight new isoperimetric bounds for certain classes of hyperbolic graphs. This establishes the vertex isoperimetric constant for all triangular and square hyperbolic lattices, answering a question of Lyons

    更新日期:2020-06-25
  • Every planar graph with the Liouville property is amenable
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-07
    Johannes Carmesin; Agelos Georgakopoulos

    We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the existence of Dirichlet harmonic function s proved by Benjamini and Schramm. As a corollary we obtain that every planar nonamenable graph admits nonconstant Dirichlet harmonic function s27.

    更新日期:2020-06-07
  • Information percolation and cutoff for the random‐cluster model
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-06-05
    Shirshendu Ganguly; Insuk Seo

    We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the

    更新日期:2020-06-05
  • Diameter of P.A. random graphs with edge‐step functions
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-26
    Caio Alves; Rodrigo Ribeiro; Rémy Sanchis

    In this work we prove general bounds for the diameter of random graphs generated by a preferential attachment model whose parameter is a function f:N→[0,1] that drives the asymptotic proportion between the numbers of vertices and edges. These results are sharp when f is a regularly varying function at infinity with strictly negative index of regular variation −γ. For this particular class, we prove

    更新日期:2020-05-26
  • Projections of the Aldous chain on binary trees: Intertwining and consistency
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-23
    Noah Forman; Soumik Pal; Douglas Rizzolo; Matthias Winkel

    Consider the Aldous Markov chain on the space of rooted binary trees with n labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix 1 ≤ k

    更新日期:2020-05-23
  • Constrained percolation, Ising model, and XOR Ising model on planar lattices
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-07
    Zhongyang Li

    We study site percolation models on planar lattices including the [m ,4,n ,4] lattice and the square tilings on the Euclidean plane () or the hyperbolic plane (), satisfying certain local constraints on degree‐4 faces. These models are closely related to Ising models and XOR Ising models (product of two i.i.d Ising models) on regular tilings of or . In particular, we obtain a description of the numbers

    更新日期:2020-05-07
  • Tight bounds for popping algorithms
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-06
    Heng Guo; Kun He

    We sharpen run‐time analysis for algorithms under the partial rejection sampling framework. Our method yields improved bounds for: the cluster‐popping algorithm for approximating all‐terminal network reliability; the cycle‐popping algorithm for sampling rooted spanning trees; and the sink‐popping algorithm for sampling sink‐free orientations. In all three applications, our bounds are not only tight

    更新日期:2020-05-06
  • Invertibility via distance for noncentered random matrices with continuous distributions
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-05-01
    Konstantin Tikhomirov

    Let A be an n ×n random matrix with independent rows R 1(A ),…,R n (A ), and assume that for any i  ≤ n and any three‐dimensional linear subspace the orthogonal projection of R i (A ) onto F has distribution density satisfying (x ∈F ) for some constant C 1>0. We show that for any fixed n ×n real matrix M we have (1) where C ′ >0 is a universal constant. In particular, the above result holds if the

    更新日期:2020-05-01
  • Hyperuniform and rigid stable matchings
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-04-27
    Michael Andreas Klatt; Günter Last; D. Yogeshwaran

    We study a stable partial matching τ of the d ‐dimensional lattice with a stationary determinantal point process Ψ on Rd with intensity α >1. For instance, Ψ might be a Poisson process. The matched points from Ψ form a stationary and ergodic (under lattice shifts) point process Ψτ with intensity 1 that very much resembles Ψ for α close to 1. On the other hand Ψτ is hyperuniform and number rigid, quite

    更新日期:2020-04-27
  • Phase transitions of the Moran process and algorithmic consequences
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-10-28
    Leslie Ann Goldberg; John Lapinskas; David Richerby

    The Moran process is a random process that models the spread of genetic mutations through graphs. On connected graphs, the process eventually reaches “fixation,” where all vertices are mutants, or “extinction,” where none are. Our main result is an almost‐tight upper bound on expected absorption time. For all ϵ>0, we show that the expected absorption time on an n‐vertex graph is o(n3+ϵ). Specifically

    更新日期:2020-04-23
  • Semi‐random graph process
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-10-21
    Omri Ben‐Eliezer; Dan Hefetz; Gal Kronenberg; Olaf Parczyk; Clara Shikhelman; Miloš Stojaković

    We introduce and study a novel semi‐random multigraph process, described as follows. The process starts with an empty graph on n vertices. In every round of the process, one vertex v of the graph is picked uniformly at random and independently of all previous rounds. We then choose an additional vertex (according to a strategy of our choice) and connect it by an edge to v. For various natural monotone

    更新日期:2020-04-23
  • Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-07-25
    Shankar Bhamidi; Sanchayan Sen

    We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (1) continuum scaling limits of uniform simple connected graphs with given degree sequence and asymptotics for the number of simple connected graphs with given degree sequence under some regularity conditions, and (2) scaling limits for the

    更新日期:2020-04-23
  • Connectivity of a general class of inhomogeneous random digraphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-10-29
    Junyu Cao; Mariana Olvera‐Cravioto

    We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models includes as special cases the directed versions of the Erdős‐Rényi model, graphs with given expected degrees, the generalized random graph, and the Poissonian random

    更新日期:2020-04-23
  • Condensation in preferential attachment models with location‐based choice
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-10-02
    John Haslegrave; Jonathan Jordan; Mark Yarrow

    We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model evolves in discrete time by selecting r vertices from the graph with replacement, with probabilities proportional to their degrees plus a constant α. A new vertex

    更新日期:2020-04-23
  • Random tree recursions: Which fixed points correspond to tangible sets of trees?
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-11-14
    Tobias Johnson; Moumanti Podder; Fiona Skerman

    Let be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only if its root has children u and v such that the subtrees rooted at u and v belong to it. Let p be the probability that a Galton‐Watson tree falls in . The metaproperty makes p satisfy a fixed‐point equation, which can have multiple solutions

    更新日期:2020-04-23
  • The chromatic number of random Borsuk graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-11-05
    Matthew Kahle; Francisco Martinez‐Figueroa

    We study a model of random graph where vertices are n i.i.d. uniform random points on the unit sphere Sd in , and a pair of vertices is connected if the Euclidean distance between them is at least 2−ϵ. We are interested in the chromatic number of this graph as n tends to infinity. It is not too hard to see that if ϵ>0 is small and fixed, then the chromatic number is d+2 with high probability. We show

    更新日期:2020-04-23
  • The height of depth‐weighted random recursive trees
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-01-12
    Kevin Leckey; Dieter Mitsche; Nick Wormald

    In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex . In this model, the probability of choosing depends on its depth in the tree. In particular, we assume that there is a function such that if has depth then its probability of being chosen is proportional to . We consider the expected value of the diameter of

    更新日期:2020-04-23
  • On the maximal multiplicity of block sizes in a random set partition
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-10-09
    Ljuben R. Mutafchiev; Mladen Savov

    We study the asymptotic behavior of the maximal multiplicity Mn = Mn(σ) of the block sizes in a set partition σ of [n] = {1,2,…,n}, assuming that σ is chosen uniformly at random from the set of all such partitions. It is known that, for large n, the blocks of a random set partition are typically of size W = W(n), with WeW = n. We show that, over subsequences {nk}k ≥ 1 of the sequence of the natural

    更新日期:2020-04-23
  • Further results on random cubic planar graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2019-10-13
    Marc Noy; Clément Requilé; Juanjo Rué

    We provide precise asymptotic estimates for the number of several classes of labeled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by Bodirsky and coworkers. We revisit their work and obtain new results on the enumeration of cubic planar graphs and on random cubic planar graphs. In particular, we determine the exact

    更新日期:2020-04-23
  • Learning random points from geometric graphs or orderings
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-04-22
    Josep Díaz; Colin McDiarmid; Dieter Mitsche

    Let X v for v ∈V be a family of n iid uniform points in the square . Suppose first that we are given the random geometric graph , where vertices u and v are adjacent when the Euclidean distance d E (X u ,X v ) is at most r . Let n 3/14≪r ≪n 1/2. Given G (without geometric information), in polynomial time we can with high probability approximately reconstruct the hidden embedding, in the sense that

    更新日期:2020-04-22
  • Size of nodal domains of the eigenvectors of a graph
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-04-16
    Han Huang; Mark Rudelson

    Consider an eigenvector of the adjacency matrix of a G (n ,p ) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately

    更新日期:2020-04-16
  • Recursive functions on conditional Galton‐Watson trees
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-04-10
    Nicolas Broutin; Luc Devroye; Nicolas Fraiman

    A recursive function on a tree is a function in which each leaf has a given value, and each internal node has a value equal to a function of the number of children, the values of the children, and possibly an explicitly specified random element U . The value of the root is the key quantity of interest in general. In this study, all node values and function values are in a finite set S . In this note

    更新日期:2020-04-10
  • On the discrepancy of random matrices with many columns
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-03-26
    Cole Franks; Michael Saks

    Motivated by the Komlós conjecture in combinatorial discrepancy, we study the discrepancy of random matrices with m rows and n independent columns drawn from a bounded lattice random variable. We prove that for n at least polynomial in m , with high probability the ℓ ∞ ‐discrepancy is at most twice the ℓ ∞ ‐covering radius of the integer span of the support of the random variable. Applying this result

    更新日期:2020-03-26
  • Modularity of Erdős‐Rényi random graphs
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-03-20
    Colin McDiarmid; Fiona Skerman

    For a given graph G , each partition of the vertices has a modularity score, with higher values indicating that the partition better captures community structure in G . The modularity q ∗(G ) of the graph G is defined to be the maximum over all vertex partitions of the modularity score, and satisfies 0 ≤ q ∗(G )<1. Modularity is at the heart of the most popular algorithms for community detection. We

    更新日期:2020-03-20
  • Finding a Hamilton cycle fast on average using rotations and extensions
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-03-16
    Yahav Alon; Michael Krivelevich

    We present an algorithm CRE , which either finds a Hamilton cycle in a graph G or determines that there is no such cycle in the graph. The algorithm's expected running time over input distribution G ∼G (n ,p ) is (1+o (1))n /p , the optimal possible expected time, for . This improves upon previous results on this problem due to Gurevich and Shelah, and to Thomason.

    更新日期:2020-03-16
  • Eigenvector delocalization for non‐Hermitian random matrices and applications
    Random Struct. Algorithms (IF 1.047) Pub Date : 2020-03-12
    Kyle Luh; Sean O'Rourke

    Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent‐entry random matrices. In particular, we show that with high probability every eigenvector is delocalized, meaning any subset of its coordinates carries an appropriate proportion of its mass. Our results hold for random matrices with genuinely complex as well as real entries. As an application

    更新日期:2020-03-12
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
Springer 纳米技术权威期刊征稿
全球视野覆盖
施普林格·自然新
chemistry
3分钟学术视频演讲大赛
物理学研究前沿热点精选期刊推荐
自然职位线上招聘会
欢迎报名注册2020量子在线大会
化学领域亟待解决的问题
材料学研究精选新
GIANT
ACS ES&T Engineering
ACS ES&T Water
屿渡论文,编辑服务
ACS Publications填问卷
阿拉丁试剂right
麻省大学
西北大学
湖南大学
华东师范大学
王要兵
化学所
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
天合科研
x-mol收录
陆军军医大学
杨财广
廖矿标
试剂库存
down
wechat
bug