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Cops and robbers is EXPTIME-complete. (English) Zbl 1307.05155
Summary: We investigate the computational complexity of deciding whether $$k$$ cops can capture a robber on a graph $$G$$. A. S. Goldstein and E. M. Reingold [Theor. Comput. Sci. 143, No. 1, 93–112 (1995; Zbl 0873.68152)] conjectured that the problem is EXPTIME-complete when both $$G$$ and $$k$$ are part of the input; we prove this conjecture.

##### MSC:
 05C57 Games on graphs (graph-theoretic aspects) 91A43 Games involving graphs 91A24 Positional games (pursuit and evasion, etc.) 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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