Geodesic
On the existence of zero-sum perfect matchings of complete graphs
Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article no. 07, 11 p.

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In this paper, we prove that given a 2-edge-coloured complete graph K4n 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.
DOI : 10.26493/1855-3974.2573.90d
Keywords: Graphs, zero-sum perfect matching 
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Teeradej Kittipassorn; Panon Sinsap. On the existence of zero-sum perfect matchings of complete graphs. Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article  no. 07, 11 p. doi : 10.26493/1855-3974.2573.90d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2573.90d/

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