Tuza’s Conjecture for Binary Geometries

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-05-30 DOI:10.1137/22m1511229

Kazuhiro Nomoto, Jorn van der Pol

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1676-1685, June 2024.
Abstract. Tuza [Finite and Infinite Sets, Proc. Colloq. Math. Soc. János Bolyai 37, North Holland, 1981, p. 888] conjectured that [math] for all graphs [math], where [math] is the minimum size of an edge set whose removal makes [math] triangle-free and [math] is the maximum size of a collection of pairwise edge-disjoint triangles. Here, we generalize Tuza’s conjecture to simple binary matroids that do not contain the Fano plane as a restriction and prove that the geometric version of the conjecture holds for cographic matroids.

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二元几何的图扎猜想

SIAM 离散数学杂志》第 38 卷第 2 期第 1676-1685 页，2024 年 6 月。摘要。Tuza [Finite and Infinite Sets, Proc.Colloq.Math.Soc. János Bolyai 37，North Holland，1981，p. 888]猜想[math]为所有图[math]，其中[math]是边集的最小大小，去除该边集使[math]无三角形，[math]是成对边相异三角形集合的最大大小。在这里，我们将图扎猜想推广到不包含法诺平面作为限制条件的简单二元矩阵，并证明该猜想的几何版本在cographic矩阵中成立。

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.