학술
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Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs
arXiv Math
CC BY
이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.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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