On Circuit Valuation of Matroids

Kazuo Murota, Akihisa Tamura

研究成果: Article査読

21 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)192-225
ページ数34
ジャーナルAdvances in Applied Mathematics
26
3
DOI
出版ステータスPublished - 2001 4
外部発表はい

ASJC Scopus subject areas

  • 応用数学

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