Abstract:For positive integers π, π, π with π > π , the set-coloring Ramsey number π (π; π, π ) is the minimum π such that if every edge of the complete graph πΎπ receives a set of π colors from a palette of π colors, then there is guaranteed to be a monochromatic clique on π vertices, that is, a subset of π vertices where all of the edges between them receive a common color. In particular, the case π = 1 corresponds to the classical multicolor Ramsey number. We prove general upper and lower bounds on οΏ½… Show more
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