Generalized Ramsey theory for graphs. II. Small diagonal numbers
Authors:
Václav Chvátal and Frank Harary
Journal:
Proc. Amer. Math. Soc. 32 (1972), 389394
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 is defined as the minimum number p such that every 2coloring of the lines of the complete graph must contain a monochromatic G. This generalizes the classical diagonal Ramsey numbers . We obtain the exact value of the Ramsey number of every such graph with at most four points.
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 [2]
 , Generalized Ramsey theory for graphs. III: Small offdiagonal numbers, Pacific J. Math. (to appear). MR 0314696 (47:3248)
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 A. W. Goodman, On sets of acquaintances and strangers at any party, Amer. Math. Monthly 66 (1959), 778783. MR 21 #6335. MR 0107610 (21:6335)
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 F. Harary, Graph theory, AddisonWesley, Reading, Mass., 1969. MR 41 #1566. MR 0256911 (41:1566)
 [6]
 , The twotriangle case of the acquaintance graph, Math. Mag. (to appear). MR 0295962 (45:5023)
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DOI:
http://dx.doi.org/10.1090/S0002993919720332559X
PII:
S 00029939(1972)0332559X
Article copyright:
© Copyright 1972 American Mathematical Society
