Graphs with Large Girth and Chromatic Number are Hard for Nullstellensatz

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-11 DOI:10.1137/23m1553273

Julian Romero, Levent Tunçel

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2108-2131, September 2024.
Abstract. We study the computational efficiency of approaches, based on Hilbert’s Nullstellensatz, which use systems of linear equations for detecting noncolorability of graphs having large girth and chromatic number. We show that for every non-[math]-colorable graph with [math] vertices and girth [math], the algorithm is required to solve systems of size at least [math] in order to detect its non-[math]-colorability.

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具有较大周长和色度数的图形难以实现零点定理

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2108-2131 页，2024 年 9 月。摘要。我们研究了基于希尔伯特无效定理（Hilbert's Nullstellensatz）的方法的计算效率，这些方法使用线性方程组来检测具有大周长和大色度数的图的非可着色性。我们证明，对于每一个具有[数学]个顶点和[数学]个周长的非[数学]可着色图，为了检测其非[数学]可着色性，算法至少需要求解[数学]个大小的系统。

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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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.