Ehrhart series for Connected Simple Graphs
Combinatorics
2011-05-26 v2
Abstract
The Ehrhart ring of the edge polytope for a connected simple graph is known to coincide with the edge ring of the same graph if satisfies the odd cycle condition. This paper gives for a graph which does not satisfy the condition, a generating set of the defining ideal of the Ehrhart ring of the edge polytope, described by combinatorial information of the graph. From this result, two factoring properties of the Ehrhart series are obtained; the first one factors out bipartite biconnected components, and the second one factors out a even cycle which shares only one edge with other part of the graph. As an application of the factoring properties, the root distribution of Ehrhart polynomials for bipartite polygon trees is determined.
Cite
@article{arxiv.1102.4804,
title = {Ehrhart series for Connected Simple Graphs},
author = {Tetsushi Matsui},
journal= {arXiv preprint arXiv:1102.4804},
year = {2011}
}