Minimum -saturated graphs

A graph G is called H-saturated if it does not contain any copy of H, but for any edge e in the complement of G the graph G + e contains some H. The minimum size of an n-vertex H-saturated graph is denoted by sat ( n , H ) . We prove sat ( n , C k ) = n + n / k + O ( ( n / k 2 ) + k 2 ) holds for all n ⩾ k ⩾ 3 , where C k is a cycle with length k. jecture that our constructions are essentially optimal.