Square coloring planar graphs with automatic discharging
Combinatorics
2022-04-13 v1 Discrete Mathematics
Abstract
The discharging method is a powerful proof technique, especially for graph coloring problems. Its major downside is that it often requires lengthy case analyses, which are sometimes given to a computer for verification. However, it is much less common to use a computer to actively look for a discharging proof. In this paper, we use a Linear Programming approach to automatically look for a discharging proof. While our system is not entirely autonomous, we manage to make some progress towards Wegner's conjecture for distance- coloring of planar graphs, by showing that colors are sufficient to color at distance every planar graph with maximum degree .
Cite
@article{arxiv.2204.05791,
title = {Square coloring planar graphs with automatic discharging},
author = {Nicolas Bousquet and Lucas de Meyer and Quentin Deschamps and Théo Pierron},
journal= {arXiv preprint arXiv:2204.05791},
year = {2022}
}