A Precise Condition for Independent Transversals in Bipartite Covers

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-05-06 DOI:10.1137/23m1600384

Stijn Cambie, Penny Haxell, Ross J. Kang, Ronen Wdowinski

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1451-1461, June 2024.
Abstract. Given a bipartite graph [math] in which any vertex in [math] (resp., [math]) has degree at most [math] (resp., [math]), suppose there is a partition of [math] that is a refinement of the bipartition [math] such that the parts in [math] (resp., [math]) have size at least [math] (resp., [math]). We prove that the condition [math] is sufficient for the existence of an independent set of vertices of [math] that is simultaneously transversal to the partition and show, moreover, that this condition is sharp. This result is a bipartite refinement of two well-known results on independent transversals, one due to the second author and the other due to Szabó and Tardos.

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二方覆盖中独立横截面的精确条件

SIAM 离散数学杂志》第 38 卷第 2 期第 1451-1461 页，2024 年 6 月。摘要。给定一个双分部图[math]，其中[math]（或[math]）中的任何顶点的度最多为[math]（或[math]），假设[math]有一个分部，它是双分部[math]的细化，使得[math]（或[math]）中各部分的大小至少为[math]（或[math]）。我们证明，[math] 这个条件足以使 [math] 中存在一个独立的顶点集，而这个顶点集同时又是横切于这个分部的，此外，我们还证明了这个条件是尖锐的。这一结果是对关于独立横切的两个著名结果的双向细化，一个由第二位作者提出，另一个由 Szabó 和 Tardos 提出。

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.