A Solution to the 2/3 Conjecture

We prove a vertex domination conjecture of Erdos, Faudree, Gould, Gyarfas, Rousseau, and Schelp that for every $n$-vertex complete graph with edges colored using three colors there exists a set of at most three vertices which have at least 2n/3 neighbors in one of the colors. Our proof makes extensive use of the ideas presented in [D. Kral' et al., A new bound for the 2/3 conjecture, Combin. Probab. Comput. 22 (2013), pp. 384--393].

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