2026/07/17 by Yusong Du, Boqing Xue
#math.CO
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 C4-free refinement complementary to the edge-count bound of Araujo, Balogh and Wang.