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arXiv · 2602.08919

Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs

Gabriel Coutinho·Paula M. S. Fialho
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Abstract

We initiate the study of a multivariate graph polynomial $\Phi_G(x,y,z)$ 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 $\Phi_G$ on bounded-degree graphs, obtained via the Fern\'andez--Procacci convergence criterion for abstract polymer gases.

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Gabriel Coutinho, Paula M. S. Fialho. 2026-02-09. Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs. https://arxiv.org/abs/2602.08919

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