Work

Graphs with large chromatic number induce $3k$-cycles

Year: 2014

Type: preprint

Abstract: Answering a question of Kalai and Meshulam, we prove that graphs without induced cycles of length $3k$ 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 $H$ such that the sum of the Betti numbers of the independence complex of $H$ is also large.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1408.2172

Authors: Bonamy, Marthe, Charbit, Pierre, Thomassé, Stéphan

Institutions: Laboratoire Bordelais de Recherche en Informatique, Laboratoire de l'Informatique du Parallélisme, Institut de Recherche en Informatique Fondamentale

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2396813348

Cites:

Cited by: 10

Related to: 10