An Improved Bound on the Sizes of Matchings Guaranteeing a Rainbow Matching
نویسندگان
چکیده
A conjecture by Aharoni and Berger states that every family of n matchings of size n + 1 in a bipartite multigraph contains a rainbow matching of size n. In this paper we prove that matching sizes of ( 3 2 + o(1) ) n suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best-known one in the case where we only aim to find a rainbow matching of size n − 1. This improves previous results by Aharoni, Charbit and Howard, and Kotlar and Ziv.
منابع مشابه
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016