Bounds for Ramsey numbers of complete graphs dropping an edge

نویسندگان

  • Yusheng Li
  • Jian Shen
چکیده

Let Kn − e be a graph obtained from a complete graph of order n by dropping an edge, and let G p be a Paley graph of order p. It is shown that if G p contains no Kn−e, then r(Kn+1−e) ≥ 2p+1. For example, G1493 contains no K13 − e, so r(K14 − e) ≥ 2987, improving the old bound 2557. It is also shown that r(K2 + G) ≤ 4r(G, K2 + G)− 2, implying that r(Kn − e) ≤ 4 r(Kn−2, Kn − e)− 2. c © 2007 Elsevier Ltd. All rights reserved.

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عنوان ژورنال:
  • Eur. J. Comb.

دوره 29  شماره 

صفحات  -

تاریخ انتشار 2008