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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generalized Ramsey theory for graphs. II. Small diagonal numbers


Authors: Václav Chvátal and Frank Harary
Journal: Proc. Amer. Math. Soc. 32 (1972), 389-394
MSC: Primary 05C35
MathSciNet review: 0332559
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Abstract: Consider a finite nonnull graph G with no loops or multiple edges and no isolated points. Its Ramsey number $ r(G)$ is defined as the minimum number p such that every 2-coloring of the lines of the complete graph $ {K_p}$ must contain a monochromatic G. This generalizes the classical diagonal Ramsey numbers $ r(n,n) = r({K_n})$ . We obtain the exact value of the Ramsey number of every such graph with at most four points.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0332559-X
PII: S 0002-9939(1972)0332559-X
Article copyright: © Copyright 1972 American Mathematical Society