Nicolas Bousquet, Quentin Deschamps, Lucas De Meyer, Théo Pierron
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Abstract
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 504-528, March 2024. 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 toward Wegner’s conjecture for distance-2 coloring of planar graphs by showing that 12 colors are sufficient to color at distance 2 every planar graph with maximum degree 4.
期刊介绍：
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.
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