%T A solution to the 2/3 conjecture %V 28 %A JM Talbot %A R Baber %N 2 %P 756-766 %D 2014 %I Society for Industrial and Applied Mathematics %J SIAM Journal on Discrete Mathematics %K Vertex domination, Ramsey theory %L discovery1529895 %X We prove a vertex domination conjecture of ErdËos, Faudree, Gould, Gy´arf´as, 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. Kr´al’ et al., A new bound for the 2/3 conjecture, Combin. Probab. Comput. 22 (2013), pp. 384–393]. %O This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.