2010/07/15 by Amini, Omid · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1007.2456
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.