- Journal Article
The r-size-Ramsey number (R) over cap (r)(H) of a graph H is the smallest number of edges a graph G can have such that for every edge-coloring of G with r colors there exists a monochromatic copy of H in G. For a graph H, we denote by H-q the graph obtained from H by subdividing its edges with q - 1 vertices each. In a recent paper of Kohayakawa, Retter and Rodl, it is shown that for all constant integers q, r >= 2 and every graph H on n vertices and of bounded maximum degree, the r-size-Ramsey number of H-q is at most (log n)(20(q-1))n(1+1/q), for n large enough. We improve upon this result using a significantly shorter argument by showing that (R) over cap (r)(H-q) <= O(n(1+1/q)) for any such graph H. Show more
Journal / seriesRandom Structures & Algorithms
Pages / Article No.
SubjectRamsey theory; random graphs; subdivisions
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