Generalized Ramsey numbers of cycles, paths, and hypergraphs
Abstract
Given a k-uniform hypergraph G and a set of k-uniform hypergraphs H, the generalized Ramsey number f(G,H,q) is the minimum number of colors needed to edge-color G so that every copy of every hypergraph H∈ H in G receives at least q different colors. In this note we obtain bounds, some asymptotically sharp, on several generalized Ramsey numbers, when G=Kn or G=Kn,n and H is a set of cycles or paths, and when G=Knk and H contains a clique on k+2 vertices or a tight cycle.
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