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arXiv · 2607.15549

Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs

Yusong Du·Boqing Xue
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Abstract

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.

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Yusong Du, Boqing Xue. 2026-07-17. Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs. https://arxiv.org/abs/2607.15549

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