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Paper detail

A new bound for the 2/3 conjecture

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, Gyárfás, Rousseau and Schelp in 1989, is 22. It is conjectured that three vertices suffice.

preprint2013arXivOpen access
Daniel Král'Chun-Hung LiuJean-Sébastien SereniPeter WhalenZelealem Yilma
math.CODiscrete Mathematics
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Daniel Král'Chun-Hung LiuJean-Sébastien SereniPeter WhalenZelealem Yilma

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