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arXiv · 1204.2519

A new bound for the 2/3 conjecture

Daniel Král'·Chun-Hung Liu·Jean-Sébastien Sereni·Peter Whalen·Zelealem Yilma
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Abstract

We show that any n-vertex complete graph with edges colored with three colors contains a set of at most four vertices such that the number of the neighbors of these vertices in one of the colors is at least 2n/3. The previous best value, proved by Erdos, Faudree, Gould, Gy\'arf\'as, Rousseau and Schelp in 1989, is 22. It is conjectured that three vertices suffice.

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Daniel Král', Chun-Hung Liu, Jean-Sébastien Sereni, Peter Whalen, Zelealem Yilma. 2012-04-11. A new bound for the 2/3 conjecture. https://arxiv.org/abs/1204.2519

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