Generalized Ramsey theory for graphs. II. Small diagonal numbers

Chvátal, Václav; Harary, Frank

doi:10.1090/S0002-9939-1972-0332559-X

Generalized Ramsey theory for graphs. II. Small diagonal numbers
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by Václav Chvátal and Frank Harary

Proc. Amer. Math. Soc. 32 (1972), 389-394

DOI: https://doi.org/10.1090/S0002-9939-1972-0332559-X

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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.

References

Generalized Ramsey theory for graphs

Diagonal numbers

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