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Vertex Folkman Numbers and the Minimum Degree of Minimal Ramsey Graphs
2018
SIAM Journal on Discrete Mathematics
We investigate the smallest possible minimum degree of r-color minimal Ramsey-graphs for the k-clique. In particular, we obtain a bound of the form O(k 2 log 2 k , which is tight up to a (log 2 k)-factor whenever the number r ≥ 2 of colors is fixed. This extends the work of Burr, Erdős, and Lovász who determined this extremal value for two colors and any clique size, and complements that of Fox, Grinshpun, Liebenau, Person, and Szabó who gave essentially tight bounds when the order k of the
doi:10.1137/17m1116696
fatcat:e62ftv7r7ndu5otoi3trx3ki4q