On a variation of the Ramsey number
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- by Gary Chartrand and Seymour Schuster PDF
- Trans. Amer. Math. Soc. 173 (1972), 353-362 Request permission
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 $c(5,n)$.References
- Jack E. Graver and James Yackel, Some graph theoretic results associated with Ramsey’s theorem, J. Combinatorial Theory 4 (1968), 125–175. MR 225685, DOI 10.1016/S0021-9800(68)80038-9
- Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London 1969. MR 0256911, DOI 10.21236/AD0705364 F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264-286.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 173 (1972), 353-362
- MSC: Primary 05C35
- DOI: https://doi.org/10.1090/S0002-9947-1972-0317992-9
- MathSciNet review: 0317992