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* is defined as the minimum number *p* such that every 2-coloring 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.

**[1]**V. Chvátal and F. Harary,*Generalized Ramsey theory for graphs*. I:*Diagonal numbers*, Period. Math. (to appear).**[2]**Václav Chvátal and Frank Harary,*Generalized Ramsey theory for graphs. III. Small off-diagonal numbers*, Pacific J. Math.**41**(1972), 335–345. MR**0314696****[3]**A. W. Goodman,*On sets of acquaintances and strangers at any party*, Amer. Math. Monthly**66**(1959), 778–783. MR**0107610****[4]**R. E. Greenwood and A. M. Gleason,*Combinatorial relations and chromatic graphs*, Canad. J. Math.**7**(1955), 1–7. MR**0067467****[5]**Frank Harary,*Graph theory*, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London, 1969. MR**0256911****[6]**Frank Harary,*The two-triangle case of the aquaintance graph*, Math. Mag.**45**(1972), 130–135. MR**0295962**

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

Article copyright:
© Copyright 1972
American Mathematical Society