On Circuit Valuation of Matroids

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

The concept of valuated matroids was introduced by Dress and Wenzel as a quantitative extension of the base exchange axiom for matroids. This paper gives several sets of cryptomorphically equivalent axioms of valuated matroids in terms of (R∪{-∞})-valued vectors defined on the circuits of the underlying matroid, where R is a totally ordered additive group. The dual of a valuated matroid is characterized by an orthogonality of (R∪{-∞})-valued vectors on circuits. Minty's characterization for matroids by the painting property is generalized for valuated matroids.

Original languageEnglish
Pages (from-to)192-225
Number of pages34
JournalAdvances in Applied Mathematics
Volume26
Issue number3
DOIs
Publication statusPublished - 2001 Apr 1
Externally publishedYes

    Fingerprint

Keywords

  • Bases
  • Circuits
  • Duality
  • Valuated matroids

ASJC Scopus subject areas

  • Applied Mathematics

Cite this