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Cooperative conditions for the existence of rainbow matchings

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Title
Cooperative conditions for the existence of rainbow matchings
Author(s)
Aharoni, Ron; Briggs, Joseph; Cho, Minho; Jinha Kim
Publication Date
2022-01
Journal
Electronic Journal of Combinatorics, v.29, no.1, pp.1 - 16
Publisher
Electronic Journal of Combinatorics
Abstract
© The authors.Let k > 1, and let F be a family of 2n + k − 3 non-empty sets of edges in a bipartite graph. If the union of every k members of F contains a matching of size n, then there exists an F-rainbow matching of size n. Replacing 2n + k − 3 by 2n + k − 2, the result is true also for k = 1, and it can be proved (for all k) both topologically and by a relatively simple combinatorial argument. The main effort is in gaining the last 1, which makes the result sharp.
URI
https://pr.ibs.re.kr/handle/8788114/11374
DOI
10.37236/9448
ISSN
1077-8926
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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