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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On a variation of the Ramsey number


Authors: Gary Chartrand and Seymour Schuster
Journal: Trans. Amer. Math. Soc. 173 (1972), 353-362
MSC: Primary 05C35
MathSciNet review: 0317992
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Abstract: Let $ c(m,n)$ be the least integer $ p$ such that, for any graph $ G$ of order $ p$, either $ G$ has an $ m$-cycle or its complement $ \bar G$ has an $ n$-cycle. Values of $ c(m,n)$ are established for $ m,n \leqslant 6$ and general formulas are proved for $ c(3,n),c(4,n)$, and $ c(5,n)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0317992-9
PII: S 0002-9947(1972)0317992-9
Keywords: Graph, cycle, Ramsey number, complement
Article copyright: © Copyright 1972 American Mathematical Society