Stijn Cambie, Penny Haxell, Ross J. Kang, Ronen Wdowinski
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A Precise Condition for Independent Transversals in Bipartite Covers
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.
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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