A solution of the misère Shannon switching game (Q1110463)

Let G be a graph and \(x_ 0\), \(x_ 1\) be two different vertices of G. Two players, Black and White, mark alternately non marked edges of G. White loses if and only if he marks all edges of a path connecting \(x_ 0\) and \(x_ 1\). This game is the misère version of the well-known Shannon Switching Game. We give its classification as a particular case of the classification of a more general game played on a matroid.