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 limn→∞ sat(n, F)/n exists for every F. We characterize the case when the limit exists and is smaller than 1.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics