The switching game on union of oriented matroids

Vanessa Chatelain (1) , Jorge Ramirez Alfonsin (2)

1 C&O - Equipe combinatoire et optimisation
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

In 1986, Hamidoune and Las Vergnas [3] introduced an oriented matroid version of the so-called Shannon's switching game. They conjectured that the classi cation of the directed switching game on oriented matroids is identical to the classi cation of the non-oriented version. In this note, we support this conjecture by showing its validity for an in nity class of oriented matroids obtained as unions of rank-1 and/or rank-2 uniform oriented matroids.

Mots clés: Shannon game; unoin matroids

Domaines: Combinatoire [math.CO]

Vanessa Chatelain, Jorge Ramirez Alfonsin. The switching game on union of oriented matroids. European Journal of Combinatorics, 2012, 33 (2), pp.215-219. ⟨10.1016/j.ejc.2011.08.006⟩. ⟨hal-00813159⟩