Graphs with large chromatic number induce -cycles
arXiv:1408.2172
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.
13 pages