Note on inseparability graphs of matroids having exactly one class of orientations (Q1363689)
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scientific article; zbMATH DE number 1047080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on inseparability graphs of matroids having exactly one class of orientations |
scientific article; zbMATH DE number 1047080 |
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Note on inseparability graphs of matroids having exactly one class of orientations (English)
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22 October 1997
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The oriented matroids whose inseparability graph is complete are identified as the oriented matroids of series-parallel graphs. Furthermore, the signed inseparability graph of such an oriented matroid, which records which pairs of elements are covariant resp.\ contravariant, determines the network. Reviewer's remark: The two conjectures at the end of the paper are false on the extension of \(R_{10}\) with a parallel element, whose inseparability graph has only one edge.
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oriented matroids
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regular matroids
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inseparability graphs
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series-parallel graphs
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