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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Ramsey graphs and block designs. I
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by T. D. Parsons PDF
Trans. Amer. Math. Soc. 209 (1975), 33-44 Request permission

Abstract:

This paper establishes a connection between a certain class of Ramsey numbers for graphs and the class of symmetric block designs admitting a polarity. The main case considered here relates the projective planes over Galois fields to the Ramsey numbers $R({C_4},{K_{1,n}}) = f(n)$. It is shown that, for every prime power $q,f({q^2} + 1) = {q^2} + q + 2$, and $f({q^2}) = {q^2} + q + 1$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 33-44
  • MSC: Primary 05C15; Secondary 05B05
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0396317-X
  • MathSciNet review: 0396317