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Rapport Année : 2012

A new bound for the 2/3 conjecture

Résumé

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 et al. in 1989, is 22. It is conjectured that three vertices suffice.
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Dates et versions

hal-00686989 , version 1 (11-04-2012)
hal-00686989 , version 2 (03-01-2013)

Identifiants

Citer

Daniel Král', Chun-Hung Liu, Jean-Sébastien Sereni, Peter Whalen, Zelealem Yilma. A new bound for the 2/3 conjecture. 2012. ⟨hal-00686989v1⟩

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