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  • Partial inverse min–max spanning tree problem
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-27
    Javad Tayyebi, Ali Reza Sepasian

    This paper addresses a partial inverse combinatorial optimization problem, called the partial inverse min–max spanning tree problem. For a given weighted graph G and a forest F of the graph, the problem is to modify weights at minimum cost so that a bottleneck (min–max) spanning tree of G contains the forest. In this paper, the modifications are measured by the weighted Manhattan distance. The main

    更新日期:2020-09-28
  • Single machine lot scheduling with non-uniform lot capacities and processing times
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-27
    Ying Chen, Yongxi Cheng, Guiqing Zhang

    In this paper, we investigate the single machine lot scheduling problem in which each lot contains one or more jobs (or part of jobs). Jobs with different sizes are splittable and should be processed in consecutive lots. Any completed (part of a) job is delivered to the customer on its completion. We generalize the problem studied in Zhang et al. (Inf Process Lett 142:46–51, 2019) such that lots may

    更新日期:2020-09-28
  • Subdivisions of digraphs in tournaments
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-25
    António Girão; Kamil Popielarz; Richard Snyder

    We show that for every positive integer k, any tournament with minimum out-degree at least (2+o(1))k2 contains a subdivision of the complete directed graph on k vertices, where each path of the subdivision has length at most 3. This result is best possible on the minimum out-degree condition (up to a multiplicative factor of 8), and it is tight with respect to the length of the paths. It may be viewed

    更新日期:2020-09-26
  • Towards tight(er) bounds for the Excluded Grid Theorem
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-25
    Julia Chuzhoy; Zihan Tan

    We study the Excluded Grid Theorem, a fundamental structural result in graph theory, that was proved by Robertson and Seymour in their seminal work on graph minors. The theorem states that there is a function f:Z+→Z+, such that for every integer g>0, every graph of treewidth at least f(g) contains the (g×g)-grid as a minor. For every integer g>0, let f(g) be the smallest value for which the theorem

    更新日期:2020-09-25
  • An approximation algorithm for submodular hitting set problem with linear penalties
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-25
    Shaojing Du, Suogang Gao, Bo Hou, Wen Liu

    The hitting set problem is a generalization of the vertex cover problem to hypergraphs. Xu et al. (Theor Comput Sci 630:117–125, 2016) presented a primal-dual algorithm for the submodular vertex cover problem with linear/submodular penalties. Motivated by their work, we study the submodular hitting set problem with linear penalties (SHSLP). The goal of the SHSLP is to select a vertex subset in the

    更新日期:2020-09-25
  • On Well-Dominated Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-25
    Sarah E. Anderson, Kirsti Kuenzel, Douglas F. Rall

    A graph is well-dominated if all of its minimal dominating sets have the same cardinality. It is proved that there are exactly eleven connected, well-dominated, triangle-free graphs whose domination number is at most 3. We prove that at least one of the factors is well-dominated if the Cartesian product of two graphs is well-dominated. In addition, we show that the Cartesian product of two connected

    更新日期:2020-09-25
  • Global rigidity of periodic graphs under fixed-lattice representations
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-24
    Viktória E. Kaszanitzky; Bernd Schulze; Shin-ichi Tanigawa

    In [9] Hendrickson proved that (d+1)-connectivity and redundant rigidity are necessary conditions for a generic (non-complete) bar-joint framework to be globally rigid in Rd. Jackson and Jordán [10] confirmed that these conditions are also sufficient in R2, giving a combinatorial characterization of graphs whose generic realizations in R2 are globally rigid. In this paper, we establish analogues of

    更新日期:2020-09-24
  • Relatively small counterexamples to Hedetniemi's conjecture
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-23
    Xuding Zhu

    Hedetniemi conjectured in 1966 that χ(G×H)=min⁡{χ(G),χ(H)} for all graphs G and H. Here G×H is the graph with vertex set V(G)×V(H) defined by putting (x,y) and (x′,y′) adjacent if and only if xx′∈E(G) and yy′∈E(H). This conjecture received a lot of attention in the past half century. Recently, Shitov refuted this conjecture. Let p be the minimum number of vertices in a graph of odd girth 7 and fractional

    更新日期:2020-09-23
  • Asymptotic density of graphs excluding disconnected minors
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-23
    Rohan Kapadia; Sergey Norin; Yingjie Qian

    For a graph H, letc∞(H)=limn→∞⁡max⁡|E(G)|n, where the maximum is taken over all graphs G on n vertices not containing H as a minor. Thus c∞(H) is the asymptotic maximum density of graphs not containing H as a minor. Employing a structural lemma due to Eppstein, we prove new upper bounds on c∞(H) for disconnected graphs H. In particular, we determine c∞(H) whenever H is a union of cycles. Finally, we

    更新日期:2020-09-23
  • Corrigendum to “Cycle decompositions of Kn and Kn − I” [J. Combin. Theory Ser. B 81 (1) (2001) 77–99]
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-23
    Brian Alspach; Heather Jordon

    There is error in the proof of Theorem 1.1, Subcase 2.1 of [J. Combin. Theory Ser. B 81 (1) (2001) 77–99]. Here, we fix that error.

    更新日期:2020-09-23
  • Additive non-approximability of chromatic number in proper minor-closed classes
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-23
    Zdeněk Dvořák; Ken-ichi Kawarabayashi

    Robin Thomas asked whether for every proper minor-closed class G, there exists a polynomial-time algorithm approximating the chromatic number of graphs from G up to a constant additive error independent on the class G. We show this is not the case: unless P=NP, for every integer k≥1, there is no polynomial-time algorithm to color a K4k+1-minor-free graph G using at most χ(G)+k−1 colors. More generally

    更新日期:2020-09-23
  • Refined enumeration of halved monotone triangles and applications to vertically symmetric alternating sign trapezoids
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-22
    Hans Höngesberg

    Halved monotone triangles are a generalisation of vertically symmetric alternating sign matrices (VSASMs). We provide a weighted enumeration of halved monotone triangles with respect to a parameter which generalises the number of −1s in a VSASM. Among other things, this enables us to establish a generating function for vertically symmetric alternating sign trapezoids. Our results are mainly presented

    更新日期:2020-09-22
  • An approximation algorithm for a general class of parametric optimization problems
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-22
    Cristina Bazgan, Arne Herzel, Stefan Ruzika, Clemens Thielen, Daniel Vanderpooten

    In a (linear) parametric optimization problem, the objective value of each feasible solution is an affine function of a real-valued parameter and one is interested in computing a solution for each possible value of the parameter. For many important parametric optimization problems including the parametric versions of the shortest path problem, the assignment problem, and the minimum cost flow problem

    更新日期:2020-09-22
  • Encoding Labelled p -Riordan Graphs by Words and Pattern-Avoiding Permutations
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-21
    Kittitat Iamthong, Ji-Hwan Jung, Sergey Kitaev

    The notion of a p-Riordan graph generalizes that of a Riordan graph, which, in turn, generalizes the notions of a Pascal graph and a Toeplitz graph. In this paper we introduce the notion of a p-Riordan word, and show how to encode p-Riordan graphs by p-Riordan words. For special important cases of Riordan graphs (the case \(p=2\)) and oriented Riordan graphs (the case \(p=3\)) we provide alternative

    更新日期:2020-09-21
  • On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-21
    Bradley Elliott, Ronald J. Gould, Kazuhide Hirohata

    In this paper, we consider a general degree sum condition sufficient to imply the existence of k vertex-disjoint chorded cycles in a graph G. Let \(\sigma _t(G)\) be the minimum degree sum of t independent vertices of G. We prove that if G is a graph of sufficiently large order and \(\sigma _t(G)\ge 3kt-t+1\) with \(k\ge 1\), then G contains k vertex-disjoint chorded cycles. We also show that the degree

    更新日期:2020-09-21
  • Groups with few maximal sum-free sets
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-18
    Hong Liu; Maryam Sharifzadeh

    A set of integers is sum-free if it does not contain any solution for x+y=z. Answering a question of Cameron and Erdős, Balogh, Liu, Sharifzadeh and Treglown recently proved that the number of maximal sum-free sets in {1,…,n} is Θ(2μ(n)/2), where μ(n) is the size of a largest sum-free set in {1,…,n}. They conjectured that, in contrast to the integer setting, there are abelian groups G having exponentially

    更新日期:2020-09-20
  • A gap in the slice rank of k-tensors
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-18
    Simone Costa; Marco Dalai

    The slice-rank method, introduced by Tao as a symmetrized version of the polynomial method of Croot, Lev and Pach and Ellenberg and Gijswijt, has proved to be a useful tool in a variety of combinatorial problems. Explicit tensors have been introduced in different contexts but little is known about the limitations of the method. In this paper, building upon a method presented by Tao and Sawin, it is

    更新日期:2020-09-20
  • EL-shelling on comodernistic lattices
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-18
    Tiansi Li

    We prove the equivalence of EL-shellability and the existence of recursive atom ordering independent of roots. We show that a comodernistic lattice, as defined by Schweig and Woodroofe, admits a recursive atom ordering independent of roots, therefore is EL-shellable. We also present and discuss a simpler EL-shelling on one of the most important classes of comodernistic lattice, the order congruence

    更新日期:2020-09-20
  • On local Turán problems
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-18
    Peter Frankl; Hao Huang; Vojtěch Rödl

    Since its formulation, Turán's hypergraph problems have been among the most challenging open problems in extremal combinatorics. One of them is the following: given a 3-uniform hypergraph F on n vertices in which any five vertices span at least one edge, prove that |F|≥(1/4−o(1))(n3). The construction showing that this bound would be best possible is simply (X3)∪(Y3) where X and Y evenly partition

    更新日期:2020-09-20
  • A bi-objective decision model and method for the integrated optimization of bus line planning and lane reservation
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-18
    Peng Wu, Ling Xu, Ada Che, Feng Chu

    The increasingly serious traffic congestion makes the bus system more and more inefficient. It is recognized all over the world that designing an attractive bus transit network is primordial to alleviate traffic congestion and reduce pollution, but it is a big challenge from an economic and technical point of view. In the literature, dedicated bus lanes are generally set up to improve the efficiency

    更新日期:2020-09-20
  • Spiders and their Kin: An Investigation of Stanley’s Chromatic Symmetric Function for Spiders and Related Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-19
    Angèle M. Foley, Joshua Kazdan, Larissa Kröll, Sofía Martínez Alberga, Oleksii Melnyk, Alexander Tenenbaum

    We study the chromatic symmetric functions of graph classes related to spiders, namely generalized spider graphs (line graphs of spiders), and what we call horseshoe crab graphs. We show that no two generalized spiders have the same chromatic symmetric function, thereby extending the work of Martin, Morin and Wagner. Additionally, we establish Query Text="Please confirm if the inserted city name in

    更新日期:2020-09-20
  • The Largest Coefficient of the Highest Root and the Second Smallest Exponent
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-18
    Tan Nhat Tran

    There are many different ways that the exponents of Weyl groups of irreducible root systems have been defined and put into practice. One of the most classical and algebraic definitions of the exponents is related to the eigenvalues of Coxeter elements. While the coefficients of the highest root when expressed as a linear combination of simple roots are combinatorial objects in nature, there are several

    更新日期:2020-09-20
  • On the isomorphism of certain primitive Q-polynomial not P-polynomial association schemes
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-17
    Giusy Monzillo; Alessandro Siciliano

    In 2011, Penttila and Williford constructed an infinite new family of primitive Q-polynomial 3-class association schemes, not arising from distance regular graphs, by exploring the geometry of the lines of the unitary polar space H(3,q2), q even, with respect to a symplectic polar space W(3,q) embedded in it. In a private communication to Penttila and Williford, H. Tanaka pointed out that these schemes

    更新日期:2020-09-18
  • Minimizing maximum delivery completion time for order scheduling with rejection
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-16
    Ren-Xia Chen, Shi-Sheng Li

    We study an order scheduling problem with rejection, in which each order consists of multiple product types and each product type should be manufactured on a dedicated machine. The aim is to find a solution to minimize a linear sum of the maximum delivery completion time of the accepted orders and the total penalty of the rejected orders. Even if the delivery times of all orders are zero, the problem

    更新日期:2020-09-16
  • Bipartite Independent Number and Hamilton-Biconnectedness of Bipartite Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-15
    Binlong Li

    Let G be a balanced bipartite graph with bipartite sets X, Y. We say that G is Hamilton-biconnected if there is a Hamilton path connecting any vertex in X and any vertex in Y. We define the bipartite independent number \(\alpha ^o_B(G)\) to be the maximum integer \(\alpha \) such that for any integer partition \(\alpha =s+t\), G has an independent set formed by s vertices in X and t vertices in Y.

    更新日期:2020-09-16
  • Ramsey numbers of path-matchings, covering designs, and 1-cores
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-16
    Louis DeBiasio, András Gyárfás, Gábor N. Sárközy

    A path-matching of order p is a vertex disjoint union of nontrivial paths spanning p vertices. Burr and Roberts, and Faudree and Schelp determined the 2-color Ramsey number of path-matchings. In this paper we study the multicolor Ramsey number of path-matchings. Given positive integers r,p1,…,pr, define RPM(p1,…,pr) to be the smallest integer n such that in any r-coloring of the edges of Kn there exists

    更新日期:2020-09-16
  • A linear time algorithm for the p -maxian problem on trees with distance constraint
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-14
    Trung Kien Nguyen, Nguyen Thanh Hung, Huong Nguyen-Thu

    This paper concerns the p-maxian problem on trees with an upper bound on the distance of new facilities. We first consider the case \(p = 2\) and show that the optimal objective is obtained if the constraint holds with equality. By this result, we further explore the characteristic of the optimal solution, which helps to develop a linear time algorithm to solve the constrained 2-maxian problem. The

    更新日期:2020-09-15
  • Unit Ball Graphs on Geodesic Spaces
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-15
    Masamichi Kuroda, Shuhei Tsujie

    Consider finitely many points in a geodesic space. If the distance of two points is less than a fixed threshold, then we regard these two points as “near”. Connecting near points with edges, we obtain a simple graph on the points, which is called a unit ball graph. If the space is the real line, then it is known as a unit interval graph. Unit ball graphs on a geodesic space describe geometric characteristics

    更新日期:2020-09-15
  • Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-09-14
    Zdeněk Dvořák; Daniel Král'; Robin Thomas

    Let G be a 4-critical graph with t triangles, embedded in a surface of genus g. Let c be the number of 4-cycles in G that do not bound a 2-cell face. We prove that∑fface ofG(|f|−4)≤κ(g+t+c−1) for a fixed constant κ, thus generalizing and strengthening several known results. As a corollary, we prove that every triangle-free graph G embedded in a surface of genus g contains a set of O(g) vertices such

    更新日期:2020-09-14
  • Abacus-histories and the combinatorics of creation operators
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-14
    Nicholas A. Loehr, Gregory S. Warrington

    Creation operators act on symmetric functions to build Schur functions, Hall–Littlewood polynomials, and related symmetric functions one row at a time. Haglund, Morse, Zabrocki, and others have studied more general symmetric functions Hα, Cα, and Bα obtained by applying any sequence of creation operators to 1. We develop new combinatorial models for the Schur expansions of these and related symmetric

    更新日期:2020-09-14
  • The index of Lie poset algebras
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-14
    Vincent E. Coll, Nicholas W. Mayers

    We provide general closed-form formulas for the index of type-A Lie poset algebras corresponding to posets of restricted height. Furthermore, we provide a combinatorial recipe for constructing all posets corresponding to type-A Frobenius Lie poset algebras of heights zero, one, and two. A discrete Morse theory argument establishes that the simplicial realizations of such posets are contractible. It

    更新日期:2020-09-14
  • Intersecting families in $$\left( {\begin{array}{c}{[m]}\\ \ell \end{array}}\right) \cup \left( {\begin{array}{c}{[n]}\\ k\end{array}}\right) $$ [ m ] ℓ ∪ [ n ] k
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-12
    Jun Wang, Huajun Zhang

    Let \(m,n,\ell \) and k be positive integers with \(\ell \ne k\), \(n>2k\), \(m<2\ell \) and \(n=\max \{m,n\}\ge \ell +k\). If \(\mathcal {F}\) is an intersecting family in \(\left( {\begin{array}{c}[m]\\ \ell \end{array}}\right) \cup \left( {\begin{array}{c}[n]\\ k\end{array}}\right) \), then $$\begin{aligned} |\mathcal {F}|\le \max \left\{ \left( {\begin{array}{c}m\\ \ell \end{array}}\right) , \left(

    更新日期:2020-09-13
  • On Colorful Edge Triples in Edge-Colored Complete Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-09
    Gábor Simonyi

    An edge-coloring of the complete graph \(K_n\) we call F-caring if it leaves no F-subgraph of \(K_n\) monochromatic and at the same time every subset of |V(F)| vertices contains in it at least one completely multicolored version of F. For the first two meaningful cases, when \(F=K_{1,3}\) and \(F=P_4\) we determine for infinitely many n the minimum number of colors needed for an F-caring edge-coloring

    更新日期:2020-09-10
  • Some algorithmic results for finding compatible spanning circuits in edge-colored graphs
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-04
    Zhiwei Guo, Hajo Broersma, Ruonan Li, Shenggui Zhang

    A compatible spanning circuit in a (not necessarily properly) edge-colored graph G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. Sufficient conditions for the existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and Euler tours), and polynomial-time algorithms for finding compatible Euler tours have

    更新日期:2020-09-05
  • Online maximum matching with recourse
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-03
    Spyros Angelopoulos, Christoph Dürr, Shendan Jin

    We study the online maximum matching problem in a model in which the edges are associated with a known recourse parameter k. An online algorithm for this problem has to maintain a valid matching while edges of the underlying graph are presented one after the other. At any moment the algorithm can decide to include an edge into the matching or to exclude it, under the restriction that at most k such

    更新日期:2020-09-03
  • On 0-Rotatable Graceful Caterpillars
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-03
    Atílio G. Luiz, C. N. Campos, R. Bruce Richter

    An injection \(f :V(T) \rightarrow \{0,\ldots ,|E(T)|\}\) of a tree T is a graceful labelling if \(\{|f(u)-f(v)| :uv \in E(T)\}=\{1,\ldots ,|E(T)|\}\). Tree T is 0-rotatable if, for any \(v \in V(T)\), there exists a graceful labelling f of T such that \(f(v)=0\). In this work, the following families of caterpillars are proved to be 0-rotatable: caterpillars with a perfect matching; caterpillars obtained

    更新日期:2020-09-03
  • Supereulerian Graphs with Constraints on the Matching Number and Minimum Degree
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-03
    Mansour J. Algefari, Hong-Jian Lai

    A graph is supereulerian if it has a spanning eulerian subgraph. We show that a connected simple graph G with \(n = |V(G)| \ge 2\) and \(\delta (G) \ge \alpha '(G)\) is supereulerian if and only if \(G \ne K_{1,n-1}\) if n is even or \(G \ne K_{2, n-2}\) if n is odd. Consequently, every connected simple graph G with \(\delta (G) \ge \alpha '(G)\) has a hamiltonian line graph.

    更新日期:2020-09-03
  • Ear-Slicing for Matchings in Hypergraphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-09-02
    András Sebő

    We study when a given edge of a factor-critical graph is contained in a matching avoiding exactly one, pregiven vertex of the graph. We then apply the results to always partition the vertex-set of a 3-regular, 3-uniform hypergraph into at most one triangle (hyperedge of size 3) and edges (subsets of size 2 of hyperedges), corresponding to the intuition, and providing new insight to triangle and edge

    更新日期:2020-09-03
  • Exposed circuits, linear quotients, and chordal clutters
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-03
    Anton Dochtermann

    A graph G is said to be chordal if it has no induced cycles of length four or more. In a recent preprint Culbertson, Guralnik, and Stiller give a new characterization of chordal graphs in terms of sequences of what they call ‘edge-erasures’. We show that these moves are in fact equivalent to a linear quotient ordering on IG‾, the edge ideal of the complement graph. Known results imply that IG‾ has

    更新日期:2020-09-03
  • New approximation algorithms for machine scheduling with rejection on single and parallel machine
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-01
    Peihai Liu, Xiwen Lu

    In this paper we consider three machine scheduling problems with the special feature that jobs may be rejected at a certain penalty. There are n jobs which are characterized by a release date, a processing time and a penalty. Each job is either accepted and then processed by one machine, or rejected and then a rejection penalty is paid. The objective is to minimize the maximum completion time of all

    更新日期:2020-09-02
  • Online leasing problem with price fluctuations and the second-hand transaction
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-01
    Xin Feng, Chengbin Chu

    This paper proposes an online leasing problem considering both price fluctuations and the second-hand transaction. In the studied problem, the price of the required equipment is assumed to fluctuate over time and lie in a predetermined range [1, M]. Moreover, the price between two adjacent times is controlled within an acceptable range [1/α, α]. The equipment can be sold through second-hand transaction

    更新日期:2020-09-02
  • The isomorphism problem of trees from the viewpoint of Terwilliger algebras
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-02
    Shuang-Dong Li, Yi-Zheng Fan, Tatsuro Ito, Masoud Karimi, Jing Xu

    Let Γ(x0) be a finite rooted tree, for which Γ is the underlying tree and x0 the root. Let T be the Terwilliger algebra of Γ with respect to x0. We study the structure of the principal T-module. As a result, it is shown that T recognizes the isomorphism class of Γ(x0).

    更新日期:2020-09-02
  • Bounded displacement non-equivalence in substitution tilings
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-02
    Dirk Frettlöh, Yotam Smilansky, Yaar Solomon

    In the study of aperiodic order and mathematical models of quasicrystals, questions regarding equivalence relations on Delone sets naturally arise. This work is dedicated to the bounded displacement (BD) equivalence relation, and especially to results concerning instances of non-equivalence. We present a general condition for two Delone sets to be BD non-equivalent, and apply our result to Delone sets

    更新日期:2020-09-02
  • Connectivity concerning the last two subconstituents of a Q-polynomial distance-regular graph
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-02
    S.M. Cioabă, J.H. Koolen, P. Terwilliger

    Let Γ be a Q-polynomial distance-regular graph of diameter d≥3. Fix a vertex γ of Γ and consider the subgraph induced on the union of the last two subconstituents of Γ with respect to γ. We prove that this subgraph is connected.

    更新日期:2020-09-02
  • General multiplicative Zagreb indices of trees and unicyclic graphs with given matching number
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-01
    Tomáš Vetrík, Selvaraj Balachandran

    The first general multiplicative Zagreb index of a graph G is defined as \(P_1^a (G) = \prod _{v \in V(G)} (deg_G (v))^a\) and the second general multiplicative Zagreb index is \(P_2^a (G) = \prod _{v \in V(G)} (deg_G (v))^{a \, deg_G (v)}\), where V(G) is the vertex set of G, \(deg_{G} (v)\) is the degree of v in G and \(a \ne 0\) is a real number. We present lower and upper bounds on the general

    更新日期:2020-09-01
  • The trace method for cotangent sums
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-01
    Wiktor Ejsmont, Franz Lehner

    This paper presents a combinatorial study of sums of integer powers of the cotangent. Our main tool is the realization of the cotangent values as eigenvalues of a simple self-adjoint matrix with complex integer entries. We use the trace method to draw conclusions about integer values of the sums and series expansions of the generating function to provide explicit evaluations; it is remarkable that

    更新日期:2020-09-01
  • Incremental optimization of independent sets under the reconfiguration framework
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-08-29
    Takehiro Ito, Haruka Mizuta, Naomi Nishimura, Akira Suzuki

    Suppose that we are given an independent set \(I_0\) of a graph G, and an integer \(l\ge 0\). Then, we are asked to find an independent set of G having the maximum size among independent sets that are reachable from \(I_0\) by either adding or removing a single vertex at a time such that all intermediate independent sets are of size at least \(l\). We show that this problem is PSPACE-hard even for

    更新日期:2020-08-29
  • Influence maximization problem: properties and algorithms
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-08-26
    Wenguo Yang, Yapu Zhang, Ding-Zhu Du

    The influence maximization problem has become one of the fundamental combinatorial optimization problems over the past decade due to its extensive applications in social networks. Although a \(1-1/e\) approximation ratio is easily obtained using a greedy algorithm for the submodular case, how to solve the non-submodular case and enhance the solution quality deserve further study. In this paper, based

    更新日期:2020-08-27
  • Signed Circuit Cover of Bridgeless Signed Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-08-27
    Mengmeng Xie, Chuixiang Zhou

    Let \((G, \sigma )\) be a 2-edge-connected flow-admissible signed graph. In this paper, we prove that \((G,\sigma )\) has a signed circuit cover with length at most 3|E(G)|.

    更新日期:2020-08-27
  • Minimum degree conditions for monochromatic cycle partitioning
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-08-27
    Dániel Korándi, Richard Lang, Shoham Letzter, Alexey Pokrovskiy

    A classical result of Erdős, Gyárfás and Pyber states that any r-edge-coloured complete graph has a partition into O(r2log⁡r) monochromatic cycles. Here we determine the minimum degree threshold for this property. More precisely, we show that there exists a constant c such that any r-edge-coloured graph on n vertices with minimum degree at least n/2+c⋅rlog⁡n has a partition into O(r2) monochromatic

    更新日期:2020-08-27
  • Rigidity and a common framework for mutually unbiased bases and k‐nets
    J. Comb. Des. (IF 0.731) Pub Date : 2020-08-25
    Sloan Nietert; Zsombor Szilágyi; Mihály Weiner

    Many deep connections have been observed between collections of mutually unbiased bases (MUBs) and combinatorial designs called k ‐nets (and in particular, between collections of MUBs and finite affine planes). Here we introduce the notion of a k ‐net over a C * ‐algebra, providing a common framework for both objects. In the commutative case, we recover (classical) k ‐nets, while the choice of M d

    更新日期:2020-08-26
  • On Specific Factors in Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-08-25
    Csilla Bujtás, Stanislav Jendrol’, Zsolt Tuza

    It is well known that if \(G = (V, E)\) is a connected multigraph and \(X\subset V\) is a subset of even order, then G contains a spanning forest H such that each vertex from X has an odd degree in H and all the other vertices have an even degree in H. This spanning forest may have isolated vertices. If this is not allowed in H, then the situation is much more complicated. In this paper, we study this

    更新日期:2020-08-26
  • Online scheduling of car-sharing request pairs between two locations
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-08-24
    Kelin Luo, Yinfeng Xu, Haodong Liu

    We consider an online car-sharing problem between two locations with advance bookings. Each customer submits a pair of requests, where each request specifies the pick-up time and the pick-up location: one request from A to B, and the other request from B to A, not necessary in this order. The scheduler aims to maximize the number of satisfied customers, where the schedule has to decide whether or not

    更新日期:2020-08-25
  • Compacted binary trees admit a stretched exponential
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-08-25
    Andrew Elvey Price, Wenjie Fang, Michael Wallner

    A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that the number of compacted binary trees of size n grows asymptotically likeΘ(n!4ne3a1n1/3n3/4), where a1≈−2.338 is the largest root of the Airy function. Our method involves a new two parameter recurrence which yields an algorithm

    更新日期:2020-08-25
  • On an inverse problem of Erdős, Kleitman, and Lemke
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-08-25
    Qinghai Zhong

    Let (G,1G) be a finite group and let S=g1⋅…⋅gℓ be a nonempty sequence over G. We say S is a tiny product-one sequence if its terms can be ordered such that their product equals 1G and ∑i=1ℓ1ord(gi)≤1. Let ti(G) be the smallest integer t such that every sequence S over G with |S|≥t has a tiny product-one subsequence. The direct problem is to obtain the exact value of ti(G), while the inverse problem

    更新日期:2020-08-25
  • Correction to: Properties of a q -Analogue of Zero Forcing
    Graphs Comb. (IF 0.597) Pub Date : 2020-08-24
    Steve Butler, Craig Erickson, Shaun Fallat, H. Tracy Hall, Brenda Kroschel, Jephian C.-H. Lin, Bryan Shader, Nathan Warnberg, Boting Yang

    The LaTeX control sequence \deg is interpreted differently in the authors’ and the publisher’s LaTeX setting

    更新日期:2020-08-24
  • A strengthening of Erdős-Gallai Theorem and proof of Woodall's conjecture
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-08-24
    Binlong Li, Bo Ning

    For a 2-connected graph G on n vertices and two vertices x,y∈V(G), we prove that there is an (x,y)-path of length at least k, if there are at least n−12 vertices in V(G)\{x,y} of degree at least k. This strengthens a celebrated theorem due to Erdős and Gallai in 1959. As the first application of this result, we show that a 2-connected graph with n vertices contains a cycle of length at least 2k, if

    更新日期:2020-08-24
  • Sandwich theorems and capacity bounds for non-commutative graphs
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-08-24
    G. Boreland, I.G. Todorov, A. Winter

    We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Grötschel, Lovász and Schrijver (1986) [7]. We define new non-commutative versions of the Lovász number of a graph which lead to an upper bound of the zero-error capacity of the corresponding quantum

    更新日期:2020-08-24
  • On flag-transitive 2-(v,k,2) designs
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-08-24
    Alice Devillers, Hongxue Liang, Cheryl E. Praeger, Binzhou Xia

    This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2-(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for

    更新日期:2020-08-24
  • The v-number of edge ideals
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-08-24
    Delio Jaramillo, Rafael H. Villarreal

    The aim of this work is to study the v-number of edge ideals of clutters. We relate the v-number with the regularity of edge ideals and classify W2 graphs. If the edge ideal of a graph has second symbolic power Cohen–Macaulay, we show that the graph is edge-critical.

    更新日期:2020-08-24
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