On the Caratheodory rank of polymatroid bases
Dion Gijswijt, Guus Regts
TL;DR
This paper proves that the Carathéodory rank of the set of bases of a matroid is at most equal to the size of its ground set, providing a new upper bound in matroid theory.
Contribution
The paper establishes a new upper bound on the Carathéodory rank of matroid bases, advancing understanding of their geometric and combinatorial properties.
Findings
Carathéodory rank of matroid bases is bounded by ground set size
Provides a theoretical upper bound in matroid theory
Enhances understanding of matroid base polytopes
Abstract
In this paper we prove that the Carath\'eodory rank of the set of bases of a (poly)matroid is upper bounded by the cardinality of the ground set.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Computational Geometry and Mesh Generation