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Journal of the London Mathematical Society 1978 s2-18(3):392-396; doi:10.1112/jlms/s2-18.3.392
© 1978 by London Mathematical Society
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© Oxford University Press

A Class of Ramsey Problems Involving Trees

C. C. Rousseau and J. Sheehan

Department of Mathematical Sciences, Memphis State University Memphis, Tennessee 38152, U.S.A.
Department of Mathematics, University of Aberdeen Aberdeen AB9 2TY

We consider the Ramsey number r(Ki+Formulam, T), where Ki+Formulam, T denotes the join of the complete graph of order l with the empty graph of order m and T denotes an arbitrary tree of order n. We obtain upper and lower bounds in the general case and the complete result in the path case, T ~= Pn. Also, we obtain partial results for the Ramsey number r(Bm, K1, n–1), where Bm denotes the m-book, K2+Formulam.


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