A new bound for the 2/3 conjecture
Discrete Mathematics
2013-01-04 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1204.2519,
title = {A new bound for the 2/3 conjecture},
author = {Daniel Král' and Chun-Hung Liu and Jean-Sébastien Sereni and Peter Whalen and Zelealem Yilma},
journal= {arXiv preprint arXiv:1204.2519},
year = {2013}
}