论文标题
树木最大化几乎完美的比赛数量
Trees maximizing the number of almost-perfect matchings
论文作者
论文摘要
我们表征了最大化几乎完美匹配的极端树，这些匹配涵盖了除了一两个或两个顶点，以及那些最大化强大的几乎完美匹配的匹配数量，这些匹配仅缺少一两个叶子。我们还确定了最小化最大匹配次数的树。我们将这些结果应用于加权Hosoya指数的极端问题，以选择基于顶点基准的权重函数。
We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings missing only one or two leaves. We also determine the trees that minimize the number of maximal matchings. We apply these results to extremal problems on the weighted Hosoya index for several choices of vertex-degree-based weight function.
