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  • A Harary-Sachs theorem for hypergraphs
    J. Comb. Theory B (IF 1.306) Pub Date : 2021-01-14
    Gregory J. Clark; Joshua N. Cooper

    We generalize the Harary-Sachs theorem to k-uniform hypergraphs: the codegree-d coefficient of the characteristic polynomial of a uniform hypergraph H can be expressed as a weighted sum of subgraph counts over certain multi-hypergraphs with d edges. We include a detailed description of the aforementioned multi-hypergraphs and a formula for their corresponding weights.

    更新日期:2021-01-14
  • Domination numbers and noncover complexes of hypergraphs
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-14
    Jinha Kim; Minki Kim

    Let H be a hypergraph on a finite set V. A cover of H is a set of vertices that meets all edges of H. If W is not a cover of H, then W is said to be a noncover of H. The noncover complex of H is the abstract simplicial complex whose faces are the noncovers of H. In this paper, we study homological properties of noncover complexes of hypergraphs. In particular, we obtain an upper bound on their Leray

    更新日期:2021-01-14
  • Categories of two-colored pair partitions Part II: Categories indexed by semigroups
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-14
    Alexander Mang; Moritz Weber

    Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by partitions of finite sets into disjoint subsets of cardinality two; the points of these sets are colored black or white. These categories correspond to “half-liberated

    更新日期:2021-01-14
  • Long regularly-spaced and convex sequences in dense sets of integers
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-13
    Brandon Hanson

    Let A be a set of integers which is dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex sequences in A and in A−A.

    更新日期:2021-01-13
  • Counting independent sets in regular hypergraphs
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-13
    József Balogh; Béla Bollobás; Bhargav Narayanan

    Amongst d-regular r-uniform hypergraphs on n vertices, which ones have the largest number of independent sets? While the analogous problem for graphs (originally raised by Granville) is now well-understood, it is not even clear what the correct general conjecture ought to be; our goal here is to propose such a generalisation. Lending credence to our conjecture, we verify it within the class of ‘quasi-bipartite’

    更新日期:2021-01-13
  • Maximum bisections of graphs without short even cycles
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-13
    Jing Lin; Qinghou Zeng

    A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most 1, and its size is the number of edges which go across the two parts. In this paper, motivated by several known results of Alon, Bollobás, Krivelevich and Sudakov about Max-Cut, we study maximum bisections of graphs without short even cycles. Let G be a graph on m edges without

    更新日期:2021-01-13
  • The existence of r‐golf designs
    J. Comb. Des. (IF 0.731) Pub Date : 2021-01-12
    Xiangqian Li; Yanxun Chang; Junling Zhou

    An r‐golf design of order v , briefly by r‐G(v), is a large set of idempotent Latin squares of order v (ILS ( v ) s) which contains r symmetric ILS ( v ) s and v − r − 2 2 transposed pairs of ILS ( v ) s. In this paper, we mainly consider the existence problem of r‐G(v)s. We present several recursive constructions and also display some direct constructions. As an application, several infinite classes

    更新日期:2021-01-13
  • Long cycles, heavy cycles and cycle decompositions in digraphs
    J. Comb. Theory B (IF 1.306) Pub Date : 2021-01-11
    Charlotte Knierim; Maxime Larcher; Anders Martinsson; Andreas Noever

    Hajós conjectured in 1968 that every Eulerian n-vertex graph can be decomposed into at most ⌊(n−1)/2⌋ edge-disjoint cycles. This has been confirmed for some special graph classes, but the general case remains open. In a sequence of papers by Bienia and Meyniel (1986) [1], Dean (1986) [7], and Bollobás and Scott (1996) [2] it was analogously conjectured that every directed Eulerian graph can be decomposed

    更新日期:2021-01-12
  • On the rational Turán exponents conjecture
    J. Comb. Theory B (IF 1.306) Pub Date : 2021-01-12
    Dong Yeap Kang; Jaehoon Kim; Hong Liu

    The extremal number ex(n,F) of a graph F is the maximum number of edges in an n-vertex graph not containing F as a subgraph. A real number r∈[1,2] is realisable if there exists a graph F with ex(n,F)=Θ(nr). Several decades ago, Erdős and Simonovits conjectured that every rational number in [1,2] is realisable. Despite decades of effort, the only known realisable numbers are 0,1,75,2, and the numbers

    更新日期:2021-01-12
  • Chromatic symmetric functions from the modular law
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-12
    Alex Abreu; Antonio Nigro

    In this article we show how to compute the chromatic quasisymmetric function of indifference graphs from the modular law introduced in [19]. We provide an algorithm which works for any function that satisfies this law, such as unicellular LLT polynomials. When the indifference graph has bipartite complement it reduces to a planar network, in this case, we prove that the coefficients of the chromatic

    更新日期:2021-01-12
  • Latin squares with maximal partial transversals of many lengths
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-12
    Anthony B. Evans; Adam Mammoliti; Ian M. Wanless

    A partial transversal T of a Latin square L is a set of entries of L in which each row, column and symbol is represented at most once. A partial transversal is maximal if it is not contained in a larger partial transversal. Any maximal partial transversal of a Latin square of order n has size at least ⌈n2⌉ and at most n. We say that a Latin square is omniversal if it possesses a maximal partial transversal

    更新日期:2021-01-12
  • Pentagonal geometries with block sizes 3, 4, and 5
    J. Comb. Des. (IF 0.731) Pub Date : 2021-01-11
    Anthony D. Forbes

    A pentagonal geometry PENT ( k , r ) is a partial linear space, where every line, or block, is incident with k points, every point is incident with r lines, and for each point x , there is a line incident with precisely those points that are not collinear with x . An opposite line pair in a pentagonal geometry consists of two parallel lines such that each point on one of the lines is not collinear

    更新日期:2021-01-11
  • Small weight codewords of projective geometric codes
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-08
    Sam Adriaensen; Lins Denaux

    We investigate small weight codewords of the p-ary linear code Cj,k(n,q) generated by the incidence matrix of k-spaces and j-spaces of PG(n,q) and its dual, with q a prime power and 0⩽j

    更新日期:2021-01-10
  • Constructing infinitely many half-arc-transitive covers of tetravalent graphs
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-08
    Pablo Spiga; Binzhou Xia

    We prove that, given a finite graph Σ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of Σ. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order 28 of finite connected tetravalent half-arc-transitive

    更新日期:2021-01-10
  • Approximation algorithm for the multicovering problem
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-09
    Abbass Gorgi, Mourad El Ouali, Anand Srivastav, Mohamed Hachimi

    Let \(\mathcal {H}=(V,\mathcal {E})\) be a hypergraph with maximum edge size \(\ell \) and maximum degree \(\varDelta \). For a given positive integers \(b_v\), \(v\in V\), a set multicover in \(\mathcal {H}\) is a set of edges \(C \subseteq \mathcal {E}\) such that every vertex v in V belongs to at least \(b_v\) edges in C. Set multicover is the problem of finding a minimum-cardinality set multicover

    更新日期:2021-01-10
  • Optimal conditions for connectedness of discretized sets
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-09
    Boris Brimkov, Valentin E. Brimkov

    An offset discretization of a set \(X \subset {\mathbb {R}}^n\) is obtained by taking the integer points inside a closed neighborhood of X of a certain radius. In this work we determine a minimum threshold for the offset radius, beyond which the discretization of an arbitrary (possibly disconnected) set is always connected. The obtained results hold for a broad class of disconnected subsets of \({\mathbb

    更新日期:2021-01-10
  • Wiener Indices of Maximal k -Degenerate Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2021-01-09
    Allan Bickle, Zhongyuan Che

    A graph is maximal k-degenerate if each induced subgraph has a vertex of degree at most k and adding any new edge to the graph violates this condition. In this paper, we provide sharp lower and upper bounds on Wiener indices of maximal k-degenerate graphs of order \(n \ge k \ge 1\). A graph is chordal if every induced cycle in the graph is a triangle and chordal maximal k-degenerate graphs of order

    更新日期:2021-01-10
  • Dominating set of rectangles intersecting a straight line
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-08
    Supantha Pandit

    The Minimum Dominating Set (MDS) problem is one of the well-studied problems in computer science. It is well-known that this problem is \(\mathsf {NP}\)-hard for simple geometric objects; unit disks, axis-parallel unit squares, and axis-parallel rectangles to name a few. An interesting variation of the MDS problem with rectangles is when there exists a straight line that intersects each of the given

    更新日期:2021-01-08
  • Application of optimization methods in the closed-loop supply chain: a literature review
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-07
    Luttiely Santos Oliveira, Ricardo Luiz Machado

    An essential aspect of a closed-loop supply chain (CLSC) involves its optimization. In this context, systematizing the publications on optimization methods applied in CLSC constitutes this research's primary objective. In this sense, a comprehensive literature review was carried out on 354 papers published from January 2008 to October 2020 to find future directions involving CLSC optimization. It was

    更新日期:2021-01-08
  • On the relationship between energy complexity and other boolean function measures
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-07
    Xiaoming Sun, Yuan Sun, Kewen Wu, Zhiyu Xia

    We focus on energy complexity, a Boolean function measure related closely to Boolean circuit design. Given a circuit \(\mathcal {C}\) over the standard basis \(\{\vee _2,\wedge _2,\lnot \}\), the energy complexity of \(\mathcal {C}\), denoted by \({{\,\mathrm{EC}\,}}(\mathcal {C})\), is the maximum number of its activated inner gates over all inputs. The energy complexity of a Boolean function f, denoted

    更新日期:2021-01-08
  • Some natural extensions of the parking space
    J. Comb. Theory A (IF 1.133) Pub Date : 2021-01-07
    Matjaž Konvalinka; Vasu Tewari

    We construct a family of Sn modules indexed by c∈{1,…,n} with the property that upon restriction to Sn−1 they recover the classical parking function representation of Haiman. The construction of these modules relies on an Sn-action on a set that is closely related to the set of parking functions. We compute the characters of these modules and use the resulting description to classify them up to isomorphism

    更新日期:2021-01-07
  • Secure domination in rooted product graphs
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-07
    Rangel Hernández-Ortiz, Luis Pedro Montejano, Juan Alberto Rodríguez-Velázquez

    A secure dominating set of a graph G is a dominating set S satisfying that for every vertex \(v\in V(G){\setminus } S\) there exists a neighbour \(u\in S\) of v such that \((S\cup \{v\}){\setminus } \{u\}\) is a dominating set as well. The secure domination number, denoted by \(\gamma _s(G)\), is the minimum cardinality among all secure dominating sets of G. This concept was introduced in 2005 by Cockayne

    更新日期:2021-01-07
  • On strict submodularity of social influence
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-06
    Qiufen Ni, Hongwei Du

    In this paper, we show several results about the strict submodularity of the influence spread in a social network with general threshold model if at each node, the threshold function is strictly increasing and strictly submodular.

    更新日期:2021-01-07
  • Cut-Edges and Regular Factors in Regular Graphs of Odd Degree
    Graphs Comb. (IF 0.597) Pub Date : 2020-10-30
    Alexandr V. Kostochka, André Raspaud, Bjarne Toft, Douglas B. West, Dara Zirlin

    We study 2k-factors in \((2r+1)\)-regular graphs. Hanson, Loten, and Toft proved that every \((2r+1)\)-regular graph with at most 2r cut-edges has a 2-factor. We generalize their result by proving for \(k\le (2r+1)/3\) that every \((2r+1)\)-regular graph with at most \(2r-3(k-1)\) cut-edges has a 2k-factor. Both the restriction on k and the restriction on the number of cut-edges are sharp. We characterize

    更新日期:2021-01-07
  • Quaternary complex Hadamard matrices of order 18
    J. Comb. Des. (IF 0.731) Pub Date : 2020-11-25
    Patric R. J. Östergård; William T. Paavola

    A technique for classifying Butson‐type Hadamard matrices over the complex 4th roots of unity is developed. The technique resembles the approach used by Kharaghani and Tayfeh‐Rezaie in their classification of the (real) 32 × 32 Hadamard matrices, where the search is split into parts according to matrix types. A classification of the 18 × 18 Butson‐type Hadamard matrices over the complex 4th roots of

    更新日期:2021-01-06
  • Graph decompositions in projective geometries
    J. Comb. Des. (IF 0.731) Pub Date : 2020-12-01
    Marco Buratti; Anamari Nakić; Alfred Wassermann

    Let PG ( F q v ) be the ( v − 1 ) ‐dimensional projective space over F q and let Γ be a simple graph of order q k − 1 q − 1 for some k . A 2 − ( v , Γ , λ ) design over F q is a collection ℬ of graphs (blocks) isomorphic to Γ with the following properties: the vertex set of every block is a subspace of PG ( F q v ) ; every two distinct points of PG ( F q v ) are adjacent in exactly λ blocks. This new

    更新日期:2021-01-06
  • The localization number of designs
    J. Comb. Des. (IF 0.731) Pub Date : 2020-12-07
    Anthony Bonato; Melissa A. Huggan; Trent G. Marbach

    We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph G , written ζ ( G ) , is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete

    更新日期:2021-01-06
  • Intersecting and 2‐intersecting hypergraphs with maximal covering number: The Erdős–Lovász theme revisited
    J. Comb. Des. (IF 0.731) Pub Date : 2020-12-08
    János Barát

    Erdős and Lovász noticed that an r ‐uniform intersecting hypergraph H with maximal covering number, that is, τ ( H ) = r , must have at least 8 3 r − 3 edges. There has been no improvement on this lower bound for 45 years. We try to understand the reason by studying some small cases to see whether the truth lies very close to this simple bound. Let q ( r ) denote the minimum number of edges in an intersecting

    更新日期:2021-01-06
  • Optimal pricing of crowdsourcing logistics services with social delivery capacity
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-05
    Wenjie Wang, Lei Xie

    Based on the sharing economy, crowdsourcing logistics services share social delivery freelancers instead of traditional full-time delivery employees. The optimal dynamic pricing model of crowdsourcing logistics services, which could be applied to adjust the social delivery capacity supply to meet the stochastic demand especially during the peak period, is established based on optimal control theory

    更新日期:2021-01-06
  • Novel distribution-free model and method for stochastic disassembly line balancing with limited distributional information
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-04
    Peng Hu, Feng Chu, Yunfei Fang, Peng Wu

    Recycling of end-of-life (EOL) products has drawn much attention from both researchers and practitioners over the recent decades due to the environmental protection, sustainable development and economic benefits. For an EOL product recycling system, a core problem is to separate their useful and hazardous parts by an efficient disassembly line in which there exist uncertain factors, such as stochastic

    更新日期:2021-01-05
  • Fractional Matchings, Component-Factors and Edge-Chromatic Critical Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2021-01-04
    Antje Klopp, Eckhard Steffen

    The first part of the paper studies star-cycle factors of graphs. It characterizes star-cycle factors of a graph G and proves upper bounds for the minimum number of \(K_{1,2}\)-components in a \(\{K_{1,1}, K_{1,2}, C_n:n\ge 3\}\)-factor of a graph G. Furthermore, it shows where these components are located with respect to the Gallai–Edmonds decomposition of G and it characterizes the edges which are

    更新日期:2021-01-05
  • Existence of strong difference families and constructions for eight new 2‐designs
    J. Comb. Des. (IF 0.731) Pub Date : 2021-01-04
    Xiaomiao Wang; Tao Feng; Shixin Wang

    Using group rings and characters as in the theory of abelian difference sets, some nonexistence results for strong difference families are provided. Existences of strong difference families with base block size 3 ≤ k ≤ 9 are discussed. Via strong difference families, eight 2‐ ( v , k , λ ) designs whose existences were unknown are constructed for ( v , k , λ ) ∈ { ( 3417 , 8 , 1 ) , ( 3753 , 8 , 1

    更新日期:2021-01-04
  • Group level social media popularity prediction by MRGB and Adam optimization
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-03
    Navdeep Bohra, Vishal Bhatnagar

    Social media has become a tremendous source to bring in new clients. Sharing posts for new offers/products to get extensive client engagement can be predicted by grouping the users based on their previous interactions. In this paper, we improve existing state-of-the-art techniques to predict group-level popularity by extending the data clustering approach and constraint network prediction using stochastic

    更新日期:2021-01-03
  • A Size Condition for Diameter Two Orientable Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2021-01-03
    Garner Cochran, Éva Czabarka, Peter Dankelmann, László Székely

    It was conjectured by Koh and Tay [Graphs Combin. 18(4) (2002), 745–756] that for \(n\ge 5\) every simple graph of order n and size at least \(\left( {\begin{array}{c}n\\ 2\end{array}}\right) -n+5\) has an orientation of diameter two. We prove this conjecture and hence determine for every \(n\ge 5\) the minimum value of m such that every graph of order n and size m has an orientation of diameter two

    更新日期:2021-01-03
  • On the Connectivity of Enhanced Power Graphs of Finite Groups
    Graphs Comb. (IF 0.597) Pub Date : 2021-01-03
    Sudip Bera, Hiranya Kishore Dey, Sajal Kumar Mukherjee

    This paper deals with the vertex connectivity of enhanced power graphs of finite groups. We classify all abelian groups G such that the vertex connectivity of enhanced power graph of G is 1. We derive an upper bound for the vertex connectivity of the enhanced power graph of any general abelian group G. Also we completely characterize all abelian groups G, such that the proper enhanced power graph is

    更新日期:2021-01-03
  • Measuring Similarity Between Connected Graphs: The Role of Induced Subgraphs and Complementarity Eigenvalues
    Graphs Comb. (IF 0.597) Pub Date : 2021-01-02
    Alberto Seeger, David Sossa

    This work elaborates on the old problem of measuring the degree of similarity, say \({\mathfrak {f}}(G,H)\), between a pair of connected graphs G and H, not necessarily of the same order. The choice of a similarity index \({\mathfrak {f}}\) depends essentially on the graph properties that are considered as important in a given context. As relevant information on a graph, one may consider for instance

    更新日期:2021-01-03
  • Differentially private approximate aggregation based on feature selection
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-02
    Zaobo He, Akshita Maradapu Vera Venkata Sai, Yan Huang, Daehee seo, Hanzhou Zhang, Qilong Han

    Privacy-preserving data aggregation is an important problem that has attracted extensive study. The state-of-the-art techniques for solving this problem is differential privacy, which offers a strong privacy guarantee without making strong assumptions about the attacker. However, existing solutions cannot effectively query data aggregation from high-dimensional datasets under differential privacy guarantee

    更新日期:2021-01-02
  • Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-01
    Ji-Bo Wang, Bo Cui, Ping Ji, Wei-Wei Liu

    This article studies scheduling problems with past-sequence-dependent delivery times (denoted by psddt) on a single-machine, i.e., the delivery time of a job depends on its waiting time of processing. We prove that the total (discounted) weighted completion time minimization can be solved in \(O(n\log n)\) time, where n is the number of jobs, and the weight is a position-dependent weight. For common

    更新日期:2021-01-01
  • Algorithmic complexity of outer independent Roman domination and outer independent total Roman domination
    J. Comb. Optim. (IF 0.843) Pub Date : 2021-01-01
    Abolfazl Poureidi, Mehrdad Ghaznavi, Jafar Fathali

    Let \(G=(V,E)\) be a graph. A function \(f : V \rightarrow \{0, 1, 2\}\) is an outer independent Roman dominating function (OIRDF) on a graph G if for every vertex \(v \in V\) with \(f (v) = 0\) there is a vertex u adjacent to v with \(f (u) = 2\) and \(\{x\in V:f(x)=0\}\) is an independent set. The weight of f is the value \( f(V)=\sum _{v\in V}f(v)\). An outer independent total Roman dominating function

    更新日期:2021-01-01
  • On Grundy and b-Chromatic Number of Some Families of Graphs: A Comparative Study
    Graphs Comb. (IF 0.597) Pub Date : 2021-01-01
    Zoya Masih, Manouchehr Zaker

    The Grundy and the b-chromatic number of graphs are two important chromatic parameters. The Grundy number of a graph G, denoted by \(\Gamma (G)\) is the worst case behavior of greedy (First-Fit) coloring procedure for G and the b-chromatic number \(\mathrm{{b}}(G)\) is the maximum number of colors used in any color-dominating coloring of G. Because the nature of these colorings are different they have

    更新日期:2021-01-01
  • Regular Cayley maps for dihedral groups
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-12-29
    István Kovács; Young Soo Kwon

    An orientably-regular map M is a 2-cell embedding of a finite connected graph in a closed orientable surface such that the group Aut∘M of orientation-preserving automorphisms of M acts transitively on the set of arcs. Such a map M is called a Cayley map for the finite group G if Aut∘M contains a subgroup, which is isomorphic to G and acts regularly on the set of vertices. Conder and Tucker (2014) classified

    更新日期:2020-12-29
  • The weak separation in higher dimensions
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-29
    Vladimir I. Danilov; Alexander V. Karzanov; Gleb A. Koshevoy

    For an odd integer r>0 and an integer n>r, we introduce a notion of weakly r-separated collections of subsets of [n]={1,2,…,n}. When r=1, this corresponds to the concept of weak separation introduced by Leclerc and Zelevinsky. In this paper, extending results due to Leclerc-Zelevinsky, we develop a geometric approach to establish a number of nice combinatorial properties of maximal weakly r-separated

    更新日期:2020-12-29
  • On triangles in derangement graphs
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-29
    Karen Meagher; Andriaherimanana Sarobidy Razafimahatratra; Pablo Spiga

    Given a permutation group G, the derangement graph ΓG of G is the Cayley graph with connection set the set of all derangements of G. We prove that, when G is transitive of degree at least 3, ΓG contains a triangle. The motivation for this work is the question of how large can be the ratio of the independence number of ΓG to the size of the stabilizer of a point in G. We give examples of transitive

    更新日期:2020-12-29
  • The feasible region of hypergraphs
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-12-24
    Xizhi Liu; Dhruv Mubayi

    Let F be a family of r-uniform hypergraphs. The feasible region Ω(F) of F is the set of points (x,y) in the unit square such that there exists a sequence of F-free r-uniform hypergraphs whose shadow density approaches x and whose edge density approaches y. The feasible region provides a lot of combinatorial information, for example, the supremum of y over all (x,y)∈Ω(F) is the Turán density π(F), and

    更新日期:2020-12-24
  • Kr-factors in graphs with low independence number
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-12-24
    Charlotte Knierim; Pascal Su

    A classical result by Hajnal and Szemerédi from 1970 determines the minimal degree conditions necessary to guarantee for a graph to contain a Kr-factor. Namely, any graph on n vertices, with minimum degree δ(G)≥(1−1r)n and r dividing n has a Kr-factor. This result is tight but the extremal examples are unique in that they all have a large independent set which is the bottleneck. Nenadov and Pehova

    更新日期:2020-12-24
  • The order dimension of divisibility
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-24
    David Lewis; Victor Souza

    The Dushnik-Miller dimension of a partially-ordered set P is the smallest d such that one can embed P into a product of d linear orders. We prove that the dimension of the divisibility order on the interval {1,…,n}, is equal to (log⁡n)2(log⁡log⁡n)−Θ(1) as n goes to infinity. We prove similar bounds for the 2-dimension of divisibility in {1,…,n}, where the 2-dimension of a poset P is the smallest d

    更新日期:2020-12-24
  • Modules of the 0-Hecke algebra arising from standard permuted composition tableaux
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-23
    Seung-Il Choi; Young-Hun Kim; Sun-Young Nam; Young-Tak Oh

    We study the Hn(0)-module Sασ due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux and decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable and characterize when Sασ is indecomposable. Second, we find characteristic relations among Sασ's and expand

    更新日期:2020-12-23
  • A Menger-like property of tree-cut width
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-12-22
    Archontia C. Giannopoulou; O-joung Kwon; Jean-Florent Raymond; Dimitrios M. Thilikos

    In 1990, Thomas proved that every graph admits a tree decomposition of minimum width that additionally satisfies a certain vertex-connectivity condition called leanness. This result had many uses and has been extended to several other decompositions. In this paper, we consider tree-cut decompositions, that have been introduced by Wollan (2015) as a possible edge-version of tree decompositions. We show

    更新日期:2020-12-22
  • Large families of permutations of Z n whose pairwise sums are permutations
    J. Comb. Des. (IF 0.731) Pub Date : 2020-12-22
    Bojan Bašić; Stefan Hačko

    We construct some large families of permutations of Z n such that the sum of any two permutations from a family is again a permutation of Z n (not necessarily in the same family). Our families are significantly larger than the largest such families known so far in the literature (depending on the value of n , the improvement can be as large as exponential). We also show that our families are maximal

    更新日期:2020-12-22
  • Application of multi-objective optimization algorithm for siting and sizing of distributed generations in distribution networks
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-12-21
    J. Rajalakshmi, S. Durairaj

    Multi-objective optimization for siting and sizing of Distributed Generations (DGs) is difficult because of the highly non-linear interactions of a large number of variables. Furthermore, effective optimization algorithms are often highly problem-dependent and need broad tuning, which limits their applicability to the real world. To address this issue, in this study, Multi-Objective Differential Evolution

    更新日期:2020-12-21
  • A proof of Lin's conjecture on inversion sequences avoiding patterns of relation triples
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-18
    George E. Andrews; Shane Chern

    A sequence e=e1e2⋯en of natural numbers is called an inversion sequence if 0≤ei≤i−1 for all i∈{1,2,…,n}. Recently, Martinez and Savage initiated an investigation of inversion sequences that avoid patterns of relation triples. Let ρ1, ρ2 and ρ3 be among the binary relations {<,>,≤,≥,=,≠,−}. Martinez and Savage defined In(ρ1,ρ2,ρ3) as the set of inversion sequences of length n such that there are no

    更新日期:2020-12-20
  • Toric Bruhat interval polytopes
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-18
    Eunjeong Lee; Mikiya Masuda; Seonjeong Park

    For two elements v and w of the symmetric group Sn with v≤w in Bruhat order, the Bruhat interval polytope Qv,w is the convex hull of the points (z(1),…,z(n))∈Rn with v≤z≤w. It is known that the Bruhat interval polytope Qv,w is the moment map image of the Richardson variety Xw−1v−1. We say that Qv,w is toric if the corresponding Richardson variety Xw−1v−1 is a toric variety. We show that when Qv,w is

    更新日期:2020-12-20
  • A positivity phenomenon in Elser's Gaussian-cluster percolation model
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-18
    Galen Dorpalen-Barry; Cyrus Hettle; David C. Livingston; Jeremy L. Martin; George D. Nasr; Julianne Vega; Hays Whitlatch

    Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideration of numerical graph invariants which we call Elser numbers elsk(G), where G is a connected graph and k a nonnegative integer. Elser had proven that els1(G)=0 for all G. By interpreting the Elser numbers as reduced Euler

    更新日期:2020-12-18
  • Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-12-16
    Binzhou Xia

    Half-arc-transitive graphs are a fascinating topic which connects graph theory, Riemann surfaces and group theory. Although fruitful results have been obtained over the last half a century, it is still challenging to construct half-arc-transitive graphs with prescribed vertex stabilizers. Until recently, there have been only six known connected tetravalent half-arc-transitive graphs with nonabelian

    更新日期:2020-12-16
  • On the classification of exceptional scattered polynomials
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-15
    Daniele Bartoli; Maria Montanucci

    Let f(X)∈Fqr[X] be a q-polynomial. If the Fq-subspace U={(xqt,f(x))|x∈Fqn} defines a maximum scattered linear set, then we call f(X) a scattered polynomial of index t. The asymptotic behavior of scattered polynomials of index t is an interesting open problem. In this sense, exceptional scattered polynomials of index t are those for which U is a maximum scattered linear set in PG(1,qmr) for infinitely

    更新日期:2020-12-16
  • Zero-sum subsequences in bounded-sum {−r,s}-sequences
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-12-14
    Alec Sun

    We study the problem of finding zero-sum blocks in bounded-sum sequences, which was introduced by Caro, Hansberg, and Montejano. Caro et al. determine the minimum {−1,1}-sequence length for when there exist k consecutive terms that sum to zero. We determine the corresponding minimum sequence length when the set {−1,1} is replaced by {−r,s} for arbitrary positive integers r and s. This confirms a conjecture

    更新日期:2020-12-15
  • Standard words and solutions of the word equation X12⋯Xn2=(X1⋯Xn)2
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-10-07
    Jarkko Peltomäki; Aleksi Saarela

    We consider solutions of the word equation X12⋯Xn2=(X1⋯Xn)2 such that the squares Xi2 are minimal squares found in optimal squareful infinite words. We apply a method developed by the second author for studying word equations and prove that there are exactly two families of solutions: reversed standard words and words obtained from reversed standard words by a simple substitution scheme. A particular

    更新日期:2020-12-14
  • Phase transitions from exp⁡(n1/2) to exp⁡(n2/3) in the asymptotics of banded plane partitions
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-11-17
    Wenjie Fang; Hsien-Kuei Hwang; Mihyun Kang

    We examine the asymptotics of a class of banded plane partitions under a varying bandwidth parameter m, and clarify the transitional behavior for large size n and increasing m=m(n) to be from c1n−1exp⁡(c2n1/2) to c3n−49/72exp⁡(c4n2/3+c5n1/3) for some explicit coefficients c1,…,c5. The method of proof, which is a unified saddle-point analysis for all phases, is general and can be extended to other classes

    更新日期:2020-12-14
  • Sparse Steiner triple systems of order 21
    J. Comb. Des. (IF 0.731) Pub Date : 2020-11-17
    Janne I. Kokkala; Patric R. J. Östergård

    A ( k , l ) ‐configuration is a set of l blocks on k points. For Steiner triple systems, ( l + 2 , l ) ‐configurations are of particular interest. The smallest nontrivial such configuration is the Pasch configuration, which is a ( 6 , 4 ) ‐configuration. A Steiner triple system of order v , an STS ( v ) , is r ‐sparse if it does not contain any ( l + 2 , l ) ‐configuration for 4 ≤ l ≤ r . The existence

    更新日期:2020-12-08
  • Anti‐Pasch optimal coverings with triples
    J. Comb. Des. (IF 0.731) Pub Date : 2020-11-25
    Fatih Demirkale; Diane Donovan; Mike Grannell

    It is shown that for v ≠ 7 , 8 , 11 , 12 , or 13, there exists an optimal covering with triples on v points that contains no Pasch configurations.

    更新日期:2020-12-08
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