Linear colorings of graphs
Combinatorics
2026-03-12 v2 Discrete Mathematics
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.
Cite
@article{arxiv.2505.02768,
title = {Linear colorings of graphs},
author = {Claire Hilaire and Matjaž Krnc and Martin Milanič and Jean-Florent Raymond},
journal= {arXiv preprint arXiv:2505.02768},
year = {2026}
}
Comments
Final version