Disjoint cycles covering specified vertices in bipartite graphs with partial degrees

Suyun Jiang and Jin Yan

Applied Mathematics and Computation, 2023, vol. 439, issue C

Abstract: Let G be a balanced bipartite graph of order 2n with bipartition (X,Y), and S a subset of X. Suppose that every pair of nonadjacent vertices {x,y} with x∈S,y∈Y satisfies dG(x)+dG(y)≥n+1. We show that if |S|≥2k+1, then G contains k disjoint cycles such that each of them contains at least two vertices of S. Moreover, if |S|≥2k+2, then G contains k disjoint cycles covering S such that each of them contains at least two vertices of S. Here, the lower bounds of |S| are necessary, and for the latter result the degree condition is sharp.

Keywords: Bipartite graphs; Disjoint cycles; Covering; Partial degree (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006993

DOI: 10.1016/j.amc.2022.127626

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