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Mixed Ramsey Numbers Revisited

Published online by Cambridge University Press:  03 December 2003

C. C. Rousseau  and
S. E. Speed
C. C. Rousseau*
Affiliation:
Department of Mathematical Sciences, The University of Memphis, 373 Dunn Hall, Memphis, Tennessee 38152-3240, USA
S. E. Speed*
Affiliation:
Department of Mathematical Sciences, The University of Memphis, 373 Dunn Hall, Memphis, Tennessee 38152-3240, USA
*
(e-mail: ccrousse@memphis.edu)
(e-mail: samspeed@memphis.edu)
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Abstract

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Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this number (i) with H fixed and , (ii) with m fixed and a sequence of dense graphs, in particular for the sequence . Open problems are mentioned throughout the paper.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 5-6: This issue contains volume twelve, parts five and six , November 2003 , pp. 653 - 660
Copyright
Copyright © Cambridge University Press 2003