Irreducibility of the Tutte polynomial of an embedded graph

Abstract

We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that the Tutte polynomial of a graph is irreducible if and only if the graph is connected and non-separable.

15 pages - this is the authors accepted manuscript / version of record without journal provided formatting

References in corpus (3)

• Graph polynomials and their applications I: The Tutte polynomial
• Types of embedded graphs and their Tutte polynomials
• Inductive tools for connected ribbon graphs, delta-matroids and multimatroids