Regular Article: Testing Orientability for Matroids is NP-Complete

Matroids and oriented matroids are fundamental objects in combinatorial geometry. While matroids model the behavior of vector configurations over general fields, oriented matroids model the behavior of vector configurations over ordered fields. For every oriented matroid there is a corresponding und...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 23; no. 1; pp. 78 - 90
Main Author Richter-Gebert, Jurgen
Format Journal Article
LanguageEnglish
Published 01.07.1999
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Summary:Matroids and oriented matroids are fundamental objects in combinatorial geometry. While matroids model the behavior of vector configurations over general fields, oriented matroids model the behavior of vector configurations over ordered fields. For every oriented matroid there is a corresponding underlying matroid. This article addresses the question how complex it is to algorithmically decide whether, on the other hand, one can assign an orientation to a given (rank 3) matroid. We will prove that this problem is NP-complete.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
content type line 23
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ISSN:0196-8858
1090-2074
DOI:10.1006/aama.1999.0648