Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs

Yusong Du; Boqing Xue

Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs

Combinatorics 2026-07-17 v1

Authors: Yusong Du , Boqing Xue

Abstract

We refine Radhakrishnan's entropy proof of the Br\'egman-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 Br\'egman 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.

Keywords

perfect matchings bipartite graphs entropy Bregman-Minc bound degree-sensitive bounds terminal-set framework

Cite

@article{arxiv.2607.15549,
  title  = {Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs},
  author = {Yusong Du and Boqing Xue},
  journal= {arXiv preprint arXiv:2607.15549},
  year   = {2026}
}

Comments

14 pages