Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs
Abstract
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.
Fields of Study & Subjects
Graph theory and applications
Advanced Graph Theory Research
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint