Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs
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| Format: | Preprint |
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2026
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| _version_ | 1866918328825544704 |
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| author | Coutinho, Gabriel Fialho, Paula M. S. |
| author_facet | Coutinho, Gabriel Fialho, Paula M. S. |
| contents | We initiate the study of a multivariate graph polynomial $Φ_G(x,y,z)$ 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 $Φ_G$ on bounded-degree graphs, obtained via the Fernández--Procacci convergence criterion for abstract polymer gases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs Coutinho, Gabriel Fialho, Paula M. S. Combinatorics 05C31 We initiate the study of a multivariate graph polynomial $Φ_G(x,y,z)$ 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 $Φ_G$ on bounded-degree graphs, obtained via the Fernández--Procacci convergence criterion for abstract polymer gases. |
| title | Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs |
| topic | Combinatorics 05C31 |
| url | https://arxiv.org/abs/2602.08919 |