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Lower bounds for lower Ramsey numbers

✍ Scribed by Ralph Faudree; Ronald J. Gould; Michael S. Jacobson; Linda Lesniak

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 310 KB
Volume: 14
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190140612

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

For any graph G, let i(G) and μ;(G) denote the smallest number of vertices in a maximal independent set and maximal clique, respectively. For positive integers m and n, the lower Ramsey number s(m, n) is the largest integer p so that every graph of order p has i(G) ≤ m or μ;(G) ≤ n. In this paper we give several new lower bounds for s (m, n) as well as determine precisely the values s(1, n).

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