Characterizing the forbidden pairs for graphs to be super-edge-connected
Abstract
Let H be a set of given connected graphs. A graph G is said to be H-free if G contains no H as an induced subgraph for any H∈ H. The graph G is super-edge-connected if each minimum edge-cut isolates a vertex in G. In this paper, except for some special graphs, we characterize all forbidden subgraph sets H such that every H-free is super-edge-connected for |H|=1 and 2.
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