Journal of Computer and System Sciences
The Othello game on an n × n board is PSPACE-complete
Theoretical Computer Science
Handbook of combinatorics (vol. 2)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing a Perfect Strategy for n*n Chess Requires Time Exponential in N
Proceedings of the 8th Colloquium on Automata, Languages and Programming
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We consider combinatorial avoidance and achievement games based on graph Ramsey theory: The players take turns in coloring edges of a graph G, each player being assigned a distinct color and choosing one so far uncolored edge per move. In avoidance games, completing a monochromatic subgraph isomorphic to another graph A leads to immediate defeat or is forbidden and the first player that cannot move loses. In the avoidance+ variant, both players are free to choose more than one edge per move. In achievement games, the first player that completes a monochromatic subgraph isomorphic to A wins. We prove that general graph Ramsey avoidance, avoidance+, and achievement endgames and several variants thereof are PSPACE-complete.