Multipartite graph—Sparse graph Ramsey numbers

Abstract

The Ramsey numberr(F, G) is determined in the case whereF is an arbitrary fixed graph andG is a sufficiently large sparse connected graph with a restriction on the maximum degree of its vertices. An asymptotically correct upper bound is obtained forr(F, T) whereT is a sufficiently large, but otherwise arbitrary, tree.

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Erdős, P., Faudree, R.J., Rousseau, C.C. et al. Multipartite graph—Sparse graph Ramsey numbers. Combinatorica 5, 311–318 (1985). https://doi.org/10.1007/BF02579245

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AMS subject classification (1980)

  • 05 C 55