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math.CO2025
On integral variations for roots of the Laplacian matching polynomial of graphs
Yi Wang, Hai-Jian Cui, Sebastian M. CioabÄ
In this paper, we study the Laplacian matching polynomial of a graph and the effect of adding edges to a graph on the roots (called Laplacian matching roots) of this polynomial. In…
math.CO2025
A hypergraph Heilmann--Lieb theorem
Jiang-Chao Wan, Yi Wang, Yi-zheng Fan
The Heilmann--Lieb theorem is a fundamental theorem in algebraic combinatorics which provides a characterization of the distribution of the zeros of matching polynomials of graphs.…