Abstract
We prove a vertex domination conjecture of Erd\H os, Faudree, Gould, Gyárfás, 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 Král', Liu, Sereni, Whalen, and Yilma.
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