Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs
Combinatorics
2026-02-10 v1
Abstract
We initiate the study of a multivariate graph polynomial that interpolates between classical counting polynomials for matchings and for cycle structures arising in the Harary--Sachs expansion of the characteristic polynomial. We focus on analytic properties and computational consequences. Our main contribution is an explicit, degree-uniform zero-free region for on bounded-degree graphs, obtained via the Fern\'andez--Procacci convergence criterion for abstract polymer gases.
Keywords
Cite
@article{arxiv.2602.08919,
title = {Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs},
author = {Gabriel Coutinho and Paula M. S. Fialho},
journal= {arXiv preprint arXiv:2602.08919},
year = {2026}
}