Cops and Robbers is EXPTIME-complete
William B. Kinnersley

TL;DR
This paper proves that determining whether k cops can catch a robber on a graph is EXPTIME-complete, confirming a long-standing conjecture and highlighting the problem's computational difficulty.
Contribution
The paper establishes the EXPTIME-completeness of the cops and robbers problem when both the graph and the number of cops are input parameters.
Findings
The problem is proven to be EXPTIME-complete.
Confirms the conjecture by Goldstein and Reingold from 1995.
Highlights the computational complexity of pursuit-evasion games on graphs.
Abstract
We investigate the computational complexity of deciding whether k cops can capture a robber on a graph G. In 1995, Goldstein and Reingold conjectured that the problem is EXPTIME-complete when both G and k are part of the input; we prove this conjecture.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems
