On Graphs With Small Ramsey Numbers, II

There exists a constant C such that for every d-degenerate graphs G 1 and G 2 on n vertices, Ramsey number R(G 1,G 2) is at most CnΔ, where Δ is the minimum of the maximum degrees of G 1 and G 2.

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Correspondence to A. V. Kostochka*.

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* The work of this author was supported by the grants 99-01-00581 and 00-01-00916 of the Russian Foundation for Fundamental Research and the Dutch-Russian Grant NWO-047-008-006.

† The work of this author was supported by the NSF grant DMS-9704114.

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Kostochka*, A.V., Rödl†, V. On Graphs With Small Ramsey Numbers, II. Combinatorica 24, 389–401 (2004). https://doi.org/10.1007/s00493-004-0024-9

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Mathematics Subject Classification (2000):

  • 05C55
  • 05C35