%0 Journal Article %@ 0895-4801 %A Talbot, JM %A Baber, R %D 2014 %F discovery:1529895 %I Society for Industrial and Applied Mathematics %J SIAM Journal on Discrete Mathematics %K Vertex domination, Ramsey theory %N 2 %P 756-766 %T A solution to the 2/3 conjecture %U https://discovery.ucl.ac.uk/id/eprint/1529895/ %V 28 %X We prove a vertex domination conjecture of Erd˝os, 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]. %Z This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.