# Finding a princess in a palace: A pursuit-evasion problem

- Published in 2012
- Added on

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This paper solves a pursuit-evasion problem in which a prince must find a princess who is constrained to move on each day from one vertex of a finite graph to another. Unlike the related and much studied `Cops and Robbers Game', the prince has no knowledge of the position of the princess; he may, however, visit any single room he wishes on each day. We characterize the graphs for which the prince has a winning strategy, and determine, for each such graph, the minimum number of days the prince requires to guarantee to find the princess.

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### BibTeX entry

@article{FindingaprincessinapalaceApursuitevasionproblem, title = {Finding a princess in a palace: A pursuit-evasion problem}, abstract = {This paper solves a pursuit-evasion problem in which a prince must find a princess who is constrained to move on each day from one vertex of a finite graph to another. Unlike the related and much studied `Cops and Robbers Game', the prince has no knowledge of the position of the princess; he may, however, visit any single room he wishes on each day. We characterize the graphs for which the prince has a winning strategy, and determine, for each such graph, the minimum number of days the prince requires to guarantee to find the princess.}, url = {http://arxiv.org/abs/1204.5490v1 http://arxiv.org/pdf/1204.5490v1}, year = 2012, author = {John R. Britnell and Mark Wildon}, comment = {}, urldate = {2019-10-08}, archivePrefix = {arXiv}, eprint = {1204.5490}, primaryClass = {math.CO}, collections = {combinatorics,easily-explained,protocols-and-strategies,puzzles} }