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On Book-Complete Graph Ramsey Numbers

✍ Scribed by Yusheng Li; C.C. Rousseau

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 274 KB
Volume: 68
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0055

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✦ Synopsis

It is shown that a graph of order N and average degree d that does not contain the book B m =K 1 +K 1, m as a subgraph has independence number at least Nf (d ), where f (x)t(log xÂx) (x Ä ). From this result we find that the book-complete graph Ramsey number satisfies r(B m , K n ) mn 2 Âlog(nÂe). It is also shown that for every tree T m with m edges, r(K

where T m is an arbitrary tree with m edges. (If a conjecture of Erdo s and So s is true, the second result can be strengthened to r(K 1 +T m , K n ) mn 2 Âlog (nÂe).) For fixed m, these bounds are of the right order of article no.

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