Graphs with large chromatic number induce $3k$-cycles
Discrete Mathematics
2014-08-12 v1 Combinatorics
Abstract
Answering a question of Kalai and Meshulam, we prove that graphs without induced cycles of length have bounded chromatic number. This implies the very first case of a much broader question asserting that every graph with large chromatic number induces a graph such that the sum of the Betti numbers of the independence complex of is also large.
Cite
@article{arxiv.1408.2172,
title = {Graphs with large chromatic number induce $3k$-cycles},
author = {Marthe Bonamy and Pierre Charbit and Stéphan Thomassé},
journal= {arXiv preprint arXiv:1408.2172},
year = {2014}
}
Comments
13 pages