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 (8)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial
• Knot invariants and the Bollobas-Riordan polynomial of embedded graphs
• Partial duality and Bollobas and Riordan's ribbon graph polynomial
• Graph polynomials and their applications I: The Tutte polynomial
• Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs
• 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 (13)

• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• Separability and the genus of a partial dual
• Bipartite partial duals and circuits in medial graphs
• A characterization of partially dual graphs
• A Penrose polynomial for embedded graphs
• Partial duals of plane graphs, separability and the graphs of knots
• Non-orientable quasi-trees for the Bollobas-Riordan polynomial
• On a conjecture of Gross, Mansour and Tucker
• Arrow ribbon graphs
• A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan
• Topological Tutte Polynomial
• Universality for polynomial invariants on ribbon graphs with half-ribbons
• The expansion of polynomial invariants for $2$-decompositions of generalized graphs