Computer assisted discharging procedure on planar graphs: application to 2-distance coloring

TL;DR

This paper develops computational discharging techniques to analyze 2-distance coloring in planar graphs, proving that subcubic planar graphs with girth at least 8 can be colored with at most 6 colors.

Contribution

It introduces a computational framework for discharging methods and applies it to establish new bounds on 2-distance coloring of specific planar graphs.

Findings

Subcubic planar graphs with girth ≥ 8 have 2-distance chromatic number ≤ 6

Develops a computational approach for discharging proofs in graph theory

Extends the applicability of discharging techniques to coloring problems

Abstract

Using computational techniques we provide a framework for proving results on subclasses of planar graphs via discharging method. The aim of this paper is to apply these techniques to study the 2-distance coloring of planar subcubic graphs. Applying these techniques we show that every subcubic planar graph $G$ of girth at least 8 has 2-distance chromatic number at most 6.