Connectedness of certain graph coloring complexes

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-05 DOI:10.1016/j.topol.2024.108985

Nandini Nilakantan , Samir Shukla

引用次数: 0

Abstract

In this article, we consider the bipartite graphs $K_{2} \times K_{n}$ . We prove that the connectedness of the complex $Hom (K_{2} \times K_{n}, K_{m})$ is $m - n - 1$ if $m \geq n$ and $m - 3$ in all the other cases. Therefore, we show that for this class of graphs, $Hom (G, K_{m})$ is exactly $(m - d - 2)$ -connected, $m \geq n$ , where d is the maximal degree of the graph G.

查看原文本刊更多论文

某些图着色复合体的连通性

在本文中，我们考虑的是双方图 K2×Kn。我们证明，复数 Hom(K2×Kn,Km) 的连通性在 m≥n 时为 m-n-1，在所有其他情况下为 m-3。因此，我们证明了对于这一类图，Hom(G,Km) 恰好是 (m-d-2)- 连接的，m≥n，其中 d 是图 G 的最大度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.