Connectedness of certain graph coloring complexes

被引：0
|
作者：
Nilakantan, Nandini [1 ]
Shukla, Samir [2 ]
机构：
[1] Indian Inst Technol IIT Kanpur, Kanpur, India
[2] Indian Inst Technol IIT Mandi, Mandi, India
来源：
TOPOLOGY AND ITS APPLICATIONS | 2024年 / 354卷
关键词：
Neighborhood complex; Hom complex; Exponential graph; Discrete Morse theory; DISCRETE MORSE-THEORY; CONJECTURE; TOPOLOGY; LOVASZ; PROOF;
D O I：
10.1016/j.topol.2024.108985
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we consider the bipartite graphs K-2 x K-n . We prove that the connectedness of the complex Hom(K-2 x K-n, K-m) is m - n - 1 if m >= 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 >= n, where d is the maximal degree of the graph G . (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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