Abstract
Generalized Geography is an impartial two-person game played on a digraph G=( V, A). In impartial Arc (Vertex) Geography, a token is initially placed on a special start vertex, and the players alternately move the token along unused arcs (vertices) of G. The player first unable to move loses and his opponent wins. The question of who wins these games IAG and IVG is known to be PSPACE-complete. Both impartial versions with two tokens on special start vertices are proved PSPACE-complete even for DAGs but polynomial for directed trees. The partizan variations, PAG and PVG, with one token per player are PSPACE-complete even for bipartite degree-restricted digraphs. They are NP-hard for DAGs, but polynomial for directed trees.
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