On Circuit Valuation of Matroids

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticle

13 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
Externally publishedYes

Fingerprint

Matroid
Valuation
Networks (circuits)
Painting
Axiom
Orthogonality
Axioms

Keywords

  • Bases
  • Circuits
  • Duality
  • Valuated matroids

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

On Circuit Valuation of Matroids. / Murota, Kazuo; Tamura, Akihisa.

In: Advances in Applied Mathematics, Vol. 26, No. 3, 04.2001, p. 192-225.

Research output: Contribution to journalArticle

Murota, Kazuo ; Tamura, Akihisa. / On Circuit Valuation of Matroids. In: Advances in Applied Mathematics. 2001 ; Vol. 26, No. 3. pp. 192-225.
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