Lattice of integer flows and poset of strongly connected orientations

Abstract

We show that the Voronoi cells of the lattice of integer flows of a finite connected graph $G$ in the quadratic vector space of real valued flows have the following very precise combinatorics: the face poset of a Voronoi cell is isomorphic to the poset of strongly connected orientations of subgraphs of $G$. This confirms a conjecture of Caporaso and Viviani {Torelli Theorem For Graphs and Tropical Curves, Duke Math. J. 153(1) (2010), 129-171}.

12 pages

References in corpus (1)

• Torelli theorem for graphs and tropical curves

Cited by in corpus (3)

• A construction of the graphic matroid from the lattice of integer flows
• Matrix polynomials, generalized Jacobians, and graphical zonotopes
• Voronoi tilings, toric arrangements and degenerations of line bundles III