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Ramsey numbers for multiple copies of complete graphs

✍ Scribed by P. J. Lorimer; R. J. Segedin


Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
107 KB
Volume
2
Category
Article
ISSN
0364-9024

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πŸ“œ SIMILAR VOLUMES


On zero sum Ramsey numbers: Multiple cop
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## Abstract As a consequence of our main result, a theorem of Schrijver and Seymour that determines the zero sum Ramsey numbers for the family of all __r__‐hypertrees on __m__ edges and a theorem of Bialostocki and Dierker that determines the zero sum Ramsey numbers for __r__‐hypermatchings are com

Fan-complete graph Ramsey numbers
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It is shown that if G and H are arbitrary fixed graphs and n is sufficiently large, then Also, we prove that r ( K 1 +F, K,) 5 (m+o(l))&(n -+ GO) for any forest Fwhose largest component has m edges. Thus r(Fe, K,) 5 (1 + o(l))&, where Fe = K1 + CK2. We conjecture that r(Fe, K,) -&(n + cm).

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This paper establishes that the local k-Ramsey number R(K m , k -loc) is identical with the mean k-Ramsey number R(K m , k -mean). This answers part of a question raised by Caro and Tuza.

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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 xΓ‚x) (x Γ„ ). From this result we find that the book-complete graph Ramsey number satisfies r(B m , K n ) mn 2 Γ‚log(nΓ‚e). I