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Bounds for the ramsey number of a disconnected graph versus any graph

✍ Scribed by Ronald J. Gould; Michael S. Jacobson

Publisher: John Wiley and Sons
Year: 1982
Tongue: English
Weight: 200 KB
Volume: 6
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190060405

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Bounds are determined for the Ramsey number of the union of graphs versus a fixed graph H, based on the Ramsey number of the components versus H. For certain unions of graphs, the exact Ramsey number is determined. From these formulas, some new Ramsey numbers are indicated. In particular, ifmagnified image.

Where k~i~ is the number of components of order i and t~1~ (H) is the minimum order of a color class over all critical colorings of the vertices of H, thenmagnified image.

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