Bounds on the coefficients of tension and flow polynomials

  • Authors:

  • Felix Breuer;Aaron Dall

  • Affiliations:

  • Freie Universität Berlin, Berlin, Germany 14195;Universitat Politècnica de Catalunya, Barcelona, Spain 08034

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2011

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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 use 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.