# On graphs with linear Ramsey numbers

@article{Graham2000OnGW, title={On graphs with linear Ramsey numbers}, author={Ronald L. Graham and Vojtech R{\"o}dl and Andrzej Rucinski}, journal={J. Graph Theory}, year={2000}, volume={35}, pages={176-192} }

For a fixed graph H, the Ramsey number r(H) is defined to be the least integer N such that in any 2-coloring of the edges of the complete graph KN, some monochromatic copy of H is always formed. Let 𝓗(n, Δ) denote the class of graphs H having n vertices and maximum degree at most Δ. It was shown by Chvatal, Rodl, Szemeredi, and Trotter that for each ” there exists c(Δ) such that r(H) 0, and for all n and Δ, there are graphs H2 e𝓗 (n, Δ) with r(H2) > 2c2Δn, which is not so far from our upper…

## 68 Citations

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