Younjin Kim (김연진), Cycle-saturated graphs with minimum number of edges

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/k²) + k²) holds for all n≥k≥3, where C_k is a cycle with length k.
Joint work with Zoltan Füredi.