English

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

R2 v1 2026-06-21T15:14:56.359Z