• J. Comb. Optim. (IF 0.843) Pub Date : 2020-09-27

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• J. Comb. Theory A (IF 1.133) Pub Date : 2020-09-18

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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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