AI 中文总结
研究二分图中完美匹配的熵界，通过引入终端集框架改进证明，得到新的度敏感上界和单顶点终端集公式，恢复等式族并改进估计，还获得与边数界互补的无\(C_4\)细化。
AI 中文摘要
我们通过引入一个终端集框架来改进Radhakrishnan对Brégman-Minc界的熵证明，在该框架中选定的顶点最后被揭示。这给出了二分图中完美匹配数量的新的度敏感上界以及单顶点终端集的显式公式。这些界恢复了标准的Brégman等式族，并改进了对某些非均匀度序列的估计。我们还得到了与Araujo、Balogh和Wang的边数界互补的无\(C_4\)细化。
英文摘要
We refine Radhakrishnan's entropy proof of the Brégman-Minc bound by introducing a terminal-set framework in which selected vertices are revealed last. This gives new degree-sensitive upper bounds for the number of perfect matchings in bipartite graphs and an explicit formula for single-vertex terminal sets. The bounds recover the standard Brégman equality family and improve the estimate for certain nonuniform degree sequences. We also obtain a $C_4$-free refinement complementary to the edge-count bound of Araujo, Balogh and Wang.
Comments14 pages
