Emergent Mind
On the Complexity of the Misère Version of Three Games Played on Graphs
(1401.0400)
Published Jan 2, 2014
in
cs.DM
and
math.CO
Abstract
We investigate the complexity of finding a winning strategy for the mis`ere version of three games played on graphs : two variants of the game $\text{NimG}$, introduced by Stockmann in 2004 and the game $\text{Vertex Geography}$ on both directed and undirected graphs. We show that on general graphs those three games are $\text{PSPACE}$-Hard or Complete. For one $\text{PSPACE}$-Hard variant of $\text{NimG}$, we find an algorithm to compute an effective winning strategy in time $\mathcal{O}(\sqrt{|V(G)|}.|E(G)|)$ when $G$ is a bipartite graph.
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