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Lower Ramsey numbers for graphs

✍ Scribed by C.M. Mynhardt

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 380 KB
Volume: 91
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90163-v

No coin nor oath required. For personal study only.

✦ Synopsis

Let p(G) denote the smallest number of vertices in a maximal clique of the graph G, while i(G) (the independent domination number of G) denotes the smallest number of vertices in a maximal independent (i.e. independent dominating) set of G. For given integers 1 and m, the lower Ramsey number s(l, m) originally defined in [4], is the largest integer p such that every graph G of order p has p(G) <I or i(G) sm. We find an upper bound for s(l, m) which is better than the upper bound in [4] if I< ]m/2]. Combining this upper bound with a lower bound determined in [3], the numbers ~(1, m) are determined exactly.

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