2-distance (Δ+1)-coloring of sparse graphs using the potential method - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Preprints, Working Papers, ... Year : 2021

2-distance (Δ+1)-coloring of sparse graphs using the potential method

Xuan Hoang La
Mickaël Montassier

Abstract

A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance (∆ + 1)-coloring for graphs with maximum average degree less than 18 and maximum degree ∆ ≥ 7. As a corollary, every planar graph with 7 girth at least 9 and ∆ ≥ 7 admits a 2-distance (∆ + 1)-coloring. The proof uses the potential method to reduce new configurations compared to classic approaches on 2-distance coloring.

Dates and versions

lirmm-04042407 , version 1 (23-03-2023)

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Xuan Hoang La, Mickaël Montassier. 2-distance (Δ+1)-coloring of sparse graphs using the potential method. 2021. ⟨lirmm-04042407⟩
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