Abstract
If the bisection width of a 2-connected graph G of even order n is not less than n/2, i.e., if the graph satisfies the even cut condition, then G has at least 3n/2−2 edges. Here we characterize the 2-connected extremal graphs with 3n/2−2 edges for every n≥4. For n≥10 an extremal graph has two high-degree vertices, the other vertices have degree 2 and they are located on paths suspended between these poles.
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