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

• Published in 2012
In the collections
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.

### 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}
}