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Ramsey Size Linear Graphs

Published online by Cambridge University Press:  12 September 2008

Paul Erdős ,
R. J. Faudree ,
C. C. Rousseau  and
R. H. Schelp
Paul Erdős
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Budapest V, Hungary
R. J. Faudree
Affiliation:
Department of Mathematical Science, Memphis State University, Tenn. 38152USA
C. C. Rousseau
Affiliation:
Department of Mathematical Science, Memphis State University, Tenn. 38152USA
R. H. Schelp
Affiliation:
Department of Mathematical Science, Memphis State University, Tenn. 38152USA
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Abstract

A graph G is Ramsey size linear if there is a constant C such that for any graph H with n edges and no isolated vertices, the Ramsey number r(G, H) ≤ Cn. It will be shown that any graph G with p vertices and q ≥ 2p − 2 edges is not Ramsey size linear, and this bound is sharp. Also, if G is connected and q ≤ p + 1, then G is Ramsey size linear, and this bound is sharp also. Special classes of graphs will be shown to be Ramsey size linear, and bounds on the Ramsey numbers will be determined.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 4 , December 1993 , pp. 389 - 399
Copyright
Copyright © Cambridge University Press 1993

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