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.

Keywords

• Bollobás–Riordan polynomial
• delta-matroid
• irreducible
• ribbon graph
• ribbon graph polynomial
• separable
• Tutte polynomial