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Ramsey numbers for certain k-graphs

Part of: Graph theory Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Stefan A. Burr  and
Richard A. Duke
Stefan A. Burr
Affiliation:
Computer Science Department, City College, (CUNY) New York, New York 10031, U.S.A.
Richard A. Duke
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30322, U.S.A.
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Abstract

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We are interested here in the Ramsey number r(T, C), where C is a complete k-uniform hypergraph and T is a “tree-like” k-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chváta1 on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r(T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.

MSC classification

Secondary: 05C35: Extremal problems 05B35: Matroids, geometric lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 284 - 296
Copyright
Copyright © Australian Mathematical Society 1981

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