Star clusters in independence complexes of graphs

被引：24
|
作者：
Barmak, Jonathan Ariel [1 ]
机构：
[1] Kungliga Tekniska Hogskolan, Dept Math, Stockholm, Sweden
来源：
ADVANCES IN MATHEMATICS | 2013年 / 241卷
关键词：
Independence complexes; Graphs; Simplicial complexes; Homotopy types; Homotopy invariants;
D O I：
10.1016/j.aim.2013.03.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce the notion of star cluster of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen from works of Engstrom and Jonsson on the homotopy type of independence complexes of triangle-free graphs and to investigate a large number of examples which appear in the literature. We present an alternative way to study the chromatic and clique numbers of a graph from a homotopical point of view and obtain new results regarding the connectivity of independence complexes. (C) 2013 Elsevier Inc. All rights reserved.
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页码：33 / 57
页数：25
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