Garijo Royo, DeliaGoodall, AndrewNesetril, JaroslavRegts, Guus2024-05-022024-05-022022Garijo Royo, D., Goodall, A.,...,Regts, G. (2022). Polynomials and graph homomorphisms. En Handbook of the Tutte Polynomial and Related Topics (pp. 405-422). New York: Chapman and Hall/CRC.9780429161612https://hdl.handle.net/11441/157426We develop in the language of graph homomorphisms the connection between the Tutte polynomial and the state models of statistical physics. • The Tutte polynomial and homomorphism numbers. • Spin models and edge coloring models. • Connection matrices and the characterization of graph invariants arising from spin models. • Homomorphism numbers and invariants of the cycle matroid of a graph. • Graph homomorphism numbers as evaluations of graph polynomials. • Other graph polynomials from counting graph homomorphisms such as the independence polynomial, the Averbouch–Godlin–Makowsky polynomial, and the Tittmann–Averbouch–Makowsky polynomial.application/pdf17engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Graph homomorphismsTutte Polynomialinfo:eu-repo/semantics/bookPartinfo:eu-repo/semantics/openAccess