论文标题
包含给定森林的跨树木数量
Number of spanning trees containing a given forest
论文作者
论文摘要
我们认为所有跨越完整的简单图$γ$的树上的$ n $顶点上包含给定的$ m $ forest $ f $。我们表明，此类跨越树的数量，$τ（f）$，不取决于$ f $的结构，并且完全由$ f $的每个连接组件中的顶点$ q_i \，（i = 1，...，m）$确定。具体来说，$τ（f）= q_1 q_2 \ cdots q_m n^{m-2} $。
We consider all spanning trees of a complete simple graph $Γ$ on $n$ vertices that contain a given $m-$forest $F$. We show that the number of such spanning trees, $τ(F)$, doesn't depend on the structure of $F$ and is completely determined by the number of vertices $q_i \, (i=1, ..., m)$ in each connected component of $F$. Specifically, $τ(F) = q_1 q_2 \cdots q_m n^{m-2}$.
