Asymptotic results on saturated graphs

doi:10.1016/0012-365X(91)90140-W

Discrete Mathematics

Volume 87, Issue 3, 22 February 1991, Pages 309-314

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Abstract

Let F be a given graph. A graph G is called F-saturated if F [nsube] G and F ⊆ G + e for every edge e ∉ E(G), e ⊆ V(G). Denote by sat(n, F) the minimum number of edges in an F-saturated graph on n vertices. A conjecture of the second author states that lim_n→∞ sat(n, F)/n exists for every F. We characterize the case when the limit exists and is smaller than 1.

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^∗: Research supported in part by University of Louisville and in part by the “AKA” Research Fund of the Hungarian Academy of Sciences.