Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 16 December 2019Accepted: 05 May 2021Published online: 02 September 2021Keywordsconflict-free coloring, kernelization, fixed-parameter tractability, combinatorial boundsAMS Subject Headings68Q25, 05C15Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publishe...

Graph theory based methods are powerful means for representing structural systems so that their geometry and topology can be understood clearly. The combination of graph theory based methods and some metaheuristics can offer effective solutions for complex engineering optimization problems. This paper presents a Charged System Search (CSS) algorithm for the free shape optimizations of thin-wall...

In this paper, we show that if G is an l-connected claw-free graph with minimum degree at least three and l ∈ {2, 3}, then for any maximum independent set S, there exists a 2-factor in which each cycle contains at least l − 1 vertices in S.

Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.

Every n-vertex graph has two vertices with the same degree (if n ≥ 2). In general, let rep(G) be the maximum multiplicity of a vertex degree in G. An easy counting argument yields rep(G) ≥ n/(2d − 2s + 1), where d is the average degree and s is the minimum degree of G. Equality can hold when 2d is an integer, and the bound is approximately sharp in general, even when G is restricted to be a tre...

The directed power graph G?(G) of a group G is the simple digraph with vertex set such that x?y if y x. G, denoted by G(G), underlying graph. In this paper, for groups and H, following proved. If has no quasicyclic subgroup Cp? which trivial intersection every cyclic K K??Cp?, then G(G)?G(H) implies G?(G)?G?(H). particular, any two torsion-free having isomorphic graphs have graphs.