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arXiv · 2505.02768

Linear colorings of graphs

Claire Hilaire·Matjaž Krnc·Martin Milanič·Jean-Florent Raymond
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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.

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Claire Hilaire, Matjaž Krnc, Martin Milanič, Jean-Florent Raymond. 2026-03-11. Linear colorings of graphs. https://arxiv.org/abs/2505.02768

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