The switching game on unions of oriented matroids

In 1986, Hamidoune and Las Vergnas [3] introduced an oriented matroid version of the so-called Shannon’s switching game. They conjectured that the classification of the directed switching game on oriented matroids is identical to the classification of the non-oriented version. In this note, we suppo...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 33; no. 2; pp. 215 - 219
Main Authors Chatelain, Vanessa, Ramírez Alfonsín, Jorge Luis
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2012
Subjects
Classification
Combinatorial analysis
Games
Switching
Unions
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Summary:In 1986, Hamidoune and Las Vergnas [3] introduced an oriented matroid version of the so-called Shannon’s switching game. They conjectured that the classification of the directed switching game on oriented matroids is identical to the classification of the non-oriented version. In this note, we support this conjecture by showing its validity for an infinite class of oriented matroids obtained as unions of rank-1 and/or rank-2 uniform oriented matroids.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2011.08.006