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.Comment: 12 pages, 4 figures, 2 data files and proof checking code. Revised
version to appear in SIAM Journal on Discrete Mathematic
