Linear colorings of graphs

European Journal of Combinatorics 2026 Open access

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Authors: Claire Hilaire, Matjaž Krnc, Martin Milanič, Jean‐Florent Raymond
DOI: 10.1016/j.ejc.2026.104374
Cited by: 0
References: 17

Abstract

Motivated by algorithmic applications, Kun, O’Brien, Pilipczuk, and Sullivan introduced the parameter linear chromatic number as a relaxation of treedepth and proved that the two parameters are polynomially related. They conjectured that treedepth could be bounded from above by twice the linear chromatic number. In this paper we investigate the properties of linear chromatic number and provide improved bounds in several graph classes.

Fields of Study & Subjects

Advanced Graph Theory Research Graph Labeling and Dimension Problems

Publication details

Journal / source
European Journal of Combinatorics
Volume
135
Pages
104374–104374
Publication date
23 March 2026
Language
EN