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Journal of the London Mathematical Society 1981 s2-24(3):405-413; doi:10.1112/jlms/s2-24.3.405
© 1981 by London Mathematical Society
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© Oxford University Press

Ramsey Numbers Involving Graphs with Long Suspended Paths

S. A. Burr

Department of Computer Sciences, School of Engineering, City College, City University of New York New York, N.Y. 10031, U.S.A.

Let G be a graph with chromatic number {chi} and with t being the minimum number of points in any color class of any point-coloring of G with {chi} colors. Let H be any connected graph and let Hn be a graph on n points which is homeomorphic to H. It is proved that if n is large enough, the Ramsey number r(G, Hn) satisfies r(G, Hn) = ({chi} – l)(n –l) + t. It is also shown that for some G, no such result holds when Hn is a star with n points.


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