Minimum C5‐saturated graphs

A graph is C5-saturated if it has no five-cycle as a subgraph, but does contain a C5 after the addition of any new edge. We prove that the minimum number of edges in a C5 -saturated graph on n≥11 vertices is sat(n, C5)=⌈10(n−1)/7⌉−1 if n∈N0={11, 12, 13, 14, 16, 18, 20} and is ⌈10(n−1)/7⌉ if n≥11 and n∉N0. © 2009 Wiley Periodicals, Inc. J Graph Theory

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