A deletion game on hypergraphs
ARIDAM III Selected papers on Third advanced research institute of discrete applied mathematics
Recent results and questions in combinatorial game complexities
Theoretical Computer Science
Complexity, appeal and challenges of combinatorial games
Theoretical Computer Science - Algorithmic combinatorial game theory
On the Complexity of Computing Winning Strategies for Finite Poset Games
Theory of Computing Systems
Flipping the winner of a poset game
Information Processing Letters
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A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity of arbitrary finite poset games was only known to exist somewhere between NC1 and PSPACE. We resolve this discrepancy by showing that deciding the winner of an arbitrary finite poset game is PSPACE-complete. To this end, we give an explicit reduction from Node Kayles, a PSPACE-complete game in which players vie to chose an independent set in a graph.