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.
AMS subject classification (1980)05 C 55
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- R. J. Faudree, C. C. Rousseau andR. H. Schelp, Generalizations of a Ramsey result of Chvátal.The Theory and Applications of Graphs (G. Chartrand, ed.) Wiley, New York (1981), 351–361.Google Scholar