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A Note on Totally Free Matroids

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Abstract

It is known matroids obtained from a totally free uniform matroid U 2,n by a sequence of segment–cosegment and cosegment–segment exchanges are totally free (Geelen et al., in J Combin Theory Ser B 92:55–67, 2004). In this paper, we prove matroids obtained from any totally free matroid by a sequence of segment–cosegment and cosegment–segment exchanges are also totally free.

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Authors and Affiliations

  1. Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin, 300071, People’s Republic of China

    Rong Chen & Kai-Nan Xiang

Authors
  1. Rong Chen
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  2. Kai-Nan Xiang
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Correspondence to Rong Chen.

Additional information

The Project-sponsored by CNNSF (No. 10971106); by Fok Ying Tung Education Foundation (No. 101002); and by PCSIRT.

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Chen, R., Xiang, KN. A Note on Totally Free Matroids. Graphs and Combinatorics 25, 657–673 (2009). https://doi.org/10.1007/s00373-010-0885-1

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  • DOI: https://doi.org/10.1007/s00373-010-0885-1

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