A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number

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Date

2023-01

Authors

Carbonero, Alvaro
Hompe, Patrick
Moore, Benjamin
Spirkl, Sophie

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Elsevier ScienceDirect

Abstract

We prove that for every n, there is a graph G with χ(G) ≥ n and ω(G) ≤ 3 such that every induced subgraph H of G with ω(H) ≤ 2 satisfies χ(H) ≤ 4.This disproves a well-known conjecture. Our construction is a digraph with bounded clique number, large dichromatic number, and no induced directed cycles of odd length at least 5.

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The final publication is available at Elsevier via https://doi.org/10.1016/j.jctb.2022.09.001 © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

χ-Boundedness, induced subgraph, directed graph

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