关于完全图零和完美匹配的存在性

Ars Math. Contemp. Pub Date : 2020-11-02 DOI:10.26493/1855-3974.2573.90d

Teeradej Kittipassorn, Panon Sinsap

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引用次数: 5

摘要

本文证明了给定两边彩色完全图$K_{4n}$，每种颜色的边数相同，我们总能找到每种颜色的边数相等的完美匹配。这解决了Caro、Hansberg、Lauri和Zarb提出的问题。Ehard, Mohr和Rautenbach也独立地解决了这个问题。

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On the existence of zero-sum perfect matchings of complete graphs

In this paper, we prove that given a 2-edge-coloured complete graph $K_{4n}$ that has the same number of edges of each colour, we can always find a perfect matching with an equal number of edges of each colour. This solves a problem posed by Caro, Hansberg, Lauri, and Zarb. The problem is also independently solved by Ehard, Mohr, and Rautenbach.

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Ars Math. Contemp.

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