A quasi-tree expansion for the surface Tutte polynomial

TL;DR

This paper introduces a quasi-tree expansion for the surface Tutte polynomial, extending known expansions of related polynomials and providing a recursive deletion-contraction framework for pseudo-surfaces.

Contribution

It establishes a quasi-tree expansion for the surface Tutte polynomial on pseudo-surfaces, generalizing previous expansions for related polynomials.

Findings

Derived a recursive deletion-contraction relation for the surface Tutte polynomial

Established a quasi-tree expansion for the polynomial on pseudo-surfaces

Unified and extended known expansions of Bollobás-Riordan, Las Vergnas, and Krushkal polynomials

Abstract

The surface Tutte polynomial has recently been generalised to pseudo-surfaces equipping it with recursive deletion-contraction relations. We use these relations to show that this generalisation naturally possesses a quasi-tree expansion. This extends quasi-tree expansions of the Bollob\'as-Riordan, Las Vergnas and Krushkal polynomials, which we recover from our main result.