Felix Breuer's Blog

Bounds on the Coefficients of Tension and Flow Polynomials

Already two weeks ago Aaron Dall and myself got our second article together out of the door. Here is the 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.

You can find the complete article on the arXiv.