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Given a graph , we say that a graph is ‐saturated if is not a subgraph of , but the addition of any new edge to creates at least one copy of . In this paper we determine all pairs for which there is a ‐saturated graph on vertices and edges. In addition, we determine all but possible sizes for ‐vertex...
Let H be a simple graph. A graph G is called an H-saturated graph if H is not a subgraph of G, but adding any missing edge to G will 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...
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