Directed switching games II The Arborescence Game Original Research Article

The Arborescence Game is a two-player game on a connected undirected graph with a distinguished vertex xo. The two players, say Black and White, pick alternately an unplayed edge. A move of Black consists of deleting the chosen edge. A move of White consists of directing the chosen edge. White wins if and only if he forms a spanning arborescence rooted at xo. We characterize winning positions of the Arborescence Game in the case when the graph is a disjoint union of two spanning trees. General strategies follow.