Graph minors, Ehrhart theory, and a monotonicity property
Combinatorics
2025-01-10 v2
Abstract
We study the extended root polytope associated to a directed graph. We show that under the operations of deletion and contraction of an edge of the graph, none of the coefficients of the -polynomial of the associated extended root polytope increase. We examine cases when the -polynomial does not change, for instance when contracting the edges of a minimal directed join in a digraph whose lattice polytope has the Gorenstein property.
Keywords
Cite
@article{arxiv.2409.18902,
title = {Graph minors, Ehrhart theory, and a monotonicity property},
author = {Tamás Kálmán and Lilla Tóthmérész},
journal= {arXiv preprint arXiv:2409.18902},
year = {2025}
}
Comments
Added a section on Gorenstein extended root polytopes. Added an appendix