自动放电的方形着色平面图形

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-23 DOI:10.1137/22m1492623

Nicolas Bousquet, Quentin Deschamps, Lucas De Meyer, Théo Pierron

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引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 504-528 页，2024 年 3 月。摘要放电法是一种强大的证明技术，尤其适用于图着色问题。它的主要缺点是经常需要冗长的案例分析，有时需要交给计算机进行验证。然而，利用计算机主动寻找放电证明的情况却很少见。在本文中，我们使用线性规划方法来自动寻找放电证明。虽然我们的系统并非完全自主，但我们设法在实现韦格纳关于平面图距离-2着色的猜想方面取得了一些进展，证明了 12 种颜色足以在距离-2 处为最大度数为 4 的每个平面图着色。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Square Coloring Planar Graphs with Automatic Discharging

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.

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

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.