An integer analogue of Carathe´odory's theorem
Journal of Combinatorial Theory Series B
Theory of linear and integer programming
Theory of linear and integer programming
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
On greedy bases packing in matroids
European Journal of Combinatorics
Hilbert Bases, Caratheodory's Theorem and Combinatorial Optimization
Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference
Improved bound for the Carathéodory rank of the bases of a matroid
Journal of Combinatorial Theory Series B
Integer Decomposition for Polyhedra Defined by Nearly Totally Unimodular Matrices
SIAM Journal on Discrete Mathematics
Path Partitions, Cycle Covers and Integer Decomposition
Graph Theory, Computational Intelligence and Thought
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A polyhedron P has the Integer Caratheodory Property if the following holds. For any positive integer k and any integer vector w@?kP, there exist affinely independent integer vectors x"1,...,x"t@?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 totally unimodular matrix, then P and projections of P have the Integer Caratheodory Property. For the matroid base polytope this answers a question by Cunningham from 1984.