A solution to the 2/3 conjecture
Combinatorics
2014-02-28 v2
Abstract
We prove a vertex domination conjecture of Erd\H os, Faudree, Gould, Gy\'arf\'as, Rousseau, and Schelp, that for every n-vertex complete graph with edges coloured using three colours there exists a set of at most three vertices which have at least 2n/3 neighbours in one of the colours. Our proof makes extensive use of the ideas presented in "A New Bound for the 2/3 Conjecture" by Kr\'al', Liu, Sereni, Whalen, and Yilma.
Cite
@article{arxiv.1306.6202,
title = {A solution to the 2/3 conjecture},
author = {Rahil Baber and John Talbot},
journal= {arXiv preprint arXiv:1306.6202},
year = {2014}
}
Comments
12 pages, 4 figures, 2 data files and proof checking code. Revised version to appear in SIAM Journal on Discrete Mathematics