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Recent results on generalized Ramsey theory for graphs

Part of the Lecture Notes in Mathematics book series (LNM,volume 303)

Abstract

Virtually all of the known results on generalized Ramsey theory for graphs have been reported here, and the most general method of proof was brute force. There is certainly a need for more powerful and general methods, but it is not certain that these exist. Since the study of Ramsey properties of general graphs appears less intractable than that for complete graphs, this may well suggest fruitful directions for other mathematical structures such as vector spaces. The fact that generalized Ramsey theory for graphs is in its infancy is attested by more than half of the references having the status, “to appear”.

Keywords

  • Complete Graph
  • Regular Graph
  • Degree Sequence
  • Ramsey Number
  • Complementary Graph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported in part by Grant 68-1515 from the Air Force Office of Scientific Research. The author thanks A. J. Schwenk for his assistance in the preparation of this article.

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© 1972 Springer-Verlag

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Harary, F. (1972). Recent results on generalized Ramsey theory for graphs. In: Alavi, Y., Lick, D.R., White, A.T. (eds) Graph Theory and Applications. Lecture Notes in Mathematics, vol 303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067364

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  • DOI: https://doi.org/10.1007/BFb0067364

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