论文标题
关于两分图中的跨越树的数量
On the number of spanning trees in bipartite graphs
论文作者
论文摘要
在本文中，我们提出了埃伦博格的猜想，该猜想提出，对于任何两部分图，跨越树的数量不超过顶点学位的产物，而不是图形组件的大小的乘积。我们表明，对于一侧常规图，猜想是正确的（这是一个至少一个组件的顶点的所有程度相等的图形）。我们还提供了一个新的证明，证明了平等性的范围图。
In this paper, we address the Ehrenborg's conjecture which proposes that for any bipartite graph the number of spanning trees does not exceed the product of the degrees of the vertices divided by the product of the sizes of the graph components. We show that the conjecture is true for a one-side regular graph (that is a graph for which all degrees of the vertices of at least one of the components are equal). We also present a new proof of the fact that the equality holds for Ferrers graphs.
