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On exchange axioms for valuated matroids and valuated delta-matroids

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Abstract

Two further equivalent axioms are given for valuations of a matroid. Let M = (V,B) be a matroid on a finite setV with the family of basesB. For ω:B→R the following three conditions are equivalent:

A similar result is obtained for valuations of a delta-matroid.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Kyoto, Japan

    Kazuo Murota

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  1. Kazuo Murota
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Additional information

This work was done while the author was at Forschungsinstitut für Diskrete Mathematik, Universität Bonn.

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Murota, K. On exchange axioms for valuated matroids and valuated delta-matroids. Combinatorica 16, 591–596 (1996). https://doi.org/10.1007/BF01271277

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