The edge spectrum of the saturation number for small paths

LetH be a simple graph. A graph G is called anH-saturated graph ifH is not a subgraph of G, but adding any missing edge to Gwill produce a copy of H . Denote by SAT (n,H) the set of all H-saturated graphs G with order n. Then the saturation number sat(n,H) is defined as minG∈SAT (n,H) |E(G)|, and the extremal number ex(n,H) is defined as maxG∈SAT (n,H) |E(G)|. A natural question is that of whether we can find an H-saturated graph withm edges for any sat(n,H) ≤ m ≤ ex(n,H). The set of all possible values m is called the edge spectrum for H-saturated graphs. In this paperwe investigate the edge spectrum for Pi-saturated graphs, where 2 ≤ i ≤ 6. It is trivial for the case of P2 that the saturated graph must be an empty graph. © 2012 Elsevier B.V. All rights reserved.