The multivariate signed Bollobas-Riordan polynomial

Abstract

We generalise the signed Bollobas-Riordan polynomial of S. Chmutov and I. Pak [Moscow Math. J. 7 (2007), no. 3, 409-418] to a multivariate signed polynomial Z and study its properties. We prove the invariance of Z under the recently defined partial duality of S. Chmutov [J. Combinatorial Theory, Ser. B, 99 (3): 617-638, 2009] and show that the duality transformation of the multivariate Tutte polynomial is a direct consequence of it.

17 pages, 2 figures. Published version: a section added about the quasi-tree expansion of the multivariate Bollobas-Riordan polynomial

References in corpus (4)

• The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial
• Graph polynomials and their applications I: The Tutte polynomial
• Graph polynomials and their applications II: Interrelations and interpretations
• A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan

Cited by in corpus (1)

• A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan