The directed switching game on Lawrence oriented matroids

David Forge, Adrien Vieilleribière
2009 European journal of combinatorics (Print)  
The main content of the note is a proof of the conjecture of Hamidoune and Las Vergnas on the directed switching game in the case of Lawrence oriented matroids. introduced the switching game for graphs circa 1960. The game has been generalized and solved for matroids by A. Lehman [1] . A directed switching game on graphs and oriented matroids was introduced by Y. O. Hamidoune and M. Las Vergnas in 1986 [2]. They have solved it for graphic and cographic oriented matroids, and stated as a
more » ... re that the classification of the oriented game is identical to the classification of its non-oriented version. This conjecture holds for the graphic and cographic cases, but remains open for more general classes of oriented matroids. In this note, we show that it holds for the class of Lawrence oriented matroids.
doi:10.1016/j.ejc.2008.12.002 fatcat:2bwzmrfu2fbpvlh2nplk7twbi4