2022/02/27 by Zsuzsanna Dancso, Dancso, Zsuzsanna, Jongmin Lim +1
Computer Science · Mathematics · #05C21 #05C50 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2202.13265
openalex publication_date 2022/02/27 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
A 2010 result of Amini provides a way to extract information about the structure of the graph from the geometry of the Voronoi polytope of the lattice of integer flows (which determines the graph up to two-isomorphism). Specifically, Amini shows that the face poset of the Voronoi polytope is isomorphic to the poset of strongly connected orientations of subgraphs. This answers a question raised by Caporaso and Viviani, and Amini also proves a dual result for integer cuts. In this paper we generalise Amini's result to regular matroids; in this context the theorem for integer cuts becomes a direct consequence of the theorem for integer flows, by making duality explicit as matroid duality.