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The Ramsey numbers for disjoint unions of cycles

✍ Scribed by Tristan Denley

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
671 KB
Volume
149
Category
Article
ISSN
0012-365X

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✦ Synopsis

As usual, for simple graphs G and H, let the Ramsey number r(G,H) be defined as the least number n such that for any graph K of order n, either G is a subgraph of K or H is a subgraph of/(. We shall establish the values of r(aC~,bCs) and r(aCv, bC7) almost precisely (where nG is the graph consisting of n vertex disjoint copies of G) extending the work of Mizuno and Sato, who proved similar results about r(aC4, bC4). Our technique also allows us to find a general upper bound for the Ramsey number r (aC,,, aC,,,) for any a >~1, n, m >/3.

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