Polyhedra with the Integer Caratheodory Property
Combinatorics
2010-04-27 v1
Abstract
A polyhedron P has the Integer Caratheodory Property if the following holds. For any positive integer k and any integer vector w in kP, there exist affinely independent integer vectors x_1,...,x_t in P and positive integers n_1,...,n_t such that n_1+...+n_t=k and w=n_1x_1+...+n_tx_t. In this paper we prove that if P is a (poly)matroid base polytope or if P is defined by a TU matrix, then P and projections of P satisfy the integer Caratheodory property.
Keywords
Cite
@article{arxiv.1004.4552,
title = {Polyhedra with the Integer Caratheodory Property},
author = {Dion Gijswijt and Guus Regts},
journal= {arXiv preprint arXiv:1004.4552},
year = {2010}
}
Comments
12 pages