Bounds on the Coefficients of Tension and Flow Polynomials

TL;DR

This paper establishes bounds on the coefficients of flow and tension polynomials of graphs by leveraging their realization as Ehrhart polynomials of inside-out polytopes, utilizing convex ear decompositions.

Contribution

It introduces a novel approach using inside-out polytopes and convex ear decompositions to derive bounds on polynomial coefficients in graph theory.

Findings

Bounds on coefficients of flow and tension polynomials derived

Use of Ehrhart polynomials and inside-out polytopes in graph polynomials

Convex ear decompositions facilitate the bounding process

Abstract

The goal of this article is to obtain bounds on the coefficients of modular and integral flow and tension polynomials of graphs. To this end we make use of the fact that these polynomials can be realized as Ehrhart polynomials of inside-out polytopes. Inside-out polytopes come with an associated relative polytopal complex and, for a wide class of inside-out polytopes, we show that this complex has a convex ear decomposition. This leads to the desired bounds on the coefficients of these polynomials.