# On graphs with small Ramsey numbers *

@article{Kostochka2001OnGW, title={On graphs with small Ramsey numbers *}, author={Alexandr V. Kostochka and Vojtech R{\"o}dl}, journal={Journal of Graph Theory}, year={2001}, volume={37} }

Let R(G) denote the minimum integer N such that for every bicoloring of the edges of KN, at least one of the monochromatic subgraphs contains G as a subgraph. We show that for every positive integer d and each γ,0 < γ < 1, there exists k = k(d,γ) such that for every bipartite graph G = (W,U;E) with the maximum degree of vertices in W at most d and $|U|\leq |W|^{\gamma }$, $R(G)\leq k|W|$. This answers a question of Trotter. We give also a weaker bound on the Ramsey numbers of graphs whose set…

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