A new bound for the 2/3 conjecture

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, Gyárfás, Rousseau and Schelp in 1989, is 22. It is conjectured that three vertices suffice.
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Contributor : Jean-Sébastien Sereni <>
Submitted on : Thursday, January 3, 2013 - 11:03:58 AM
Last modification on : Wednesday, July 31, 2019 - 3:24:15 PM
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  • HAL Id : hal-00686989, version 2
  • ARXIV : 1204.2519

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Daniel Král', Chun-Hung Liu, Jean-Sébastien Sereni, Peter Whalen, Zelealem Yilma. A new bound for the 2/3 conjecture. [Research Report] Loria & Inria Grand Est. 2012. ⟨hal-00686989v2⟩

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