Extremal problems on saturation for the family of k-edge-connected graphs
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چکیده
Let F be a family of graphs. A graph G is F-saturated if G contains no member of F as a subgraph but G + e contains some member of F whenever e ∈ E(G). The saturation number and extremal number of F , denoted sat(n,F) and ex(n,F) respectively, are the minimum and maximum numbers of edges among n-vertex Fsaturated graphs. For k ∈ N, let Fk and F ′ k be the families of k-connected and k-edgeconnected graphs, respectively. Wenger proved sat(n,Fk) = (k − 1)n − ( k 2 ) ; we prove sat(n,F ′ k) = (k − 1)(n − 1) − ⌊
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تاریخ انتشار 2018