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 $n\ge 4$. For $n\ge 10$ an extremal graph has two high-degree vertices, the other vertices have degree 2 and they are located on paths suspended between these poles.

中文翻译：

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满足平切条件的最小2连通图

如果偶数阶n的2个连通图G的对分宽度不小于$ñ/2$即，如果图形满足均匀切割条件，则G至少具有$3ñ/2-2$边缘。这里我们用2表示极值图$3ñ/2-2$ 每个边缘 $ñ\ge 4$。对于$ñ\ge 10$一个极值图具有两个高度顶点，其他顶点具有2度，并且它们位于这些极之间的悬浮路径上。