# Catching a mouse on a tree

- Published in 2015
- Added on

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In this paper we consider a pursuit-evasion game on a graph. A team of cats, which may choose any vertex of the graph at any turn, tries to catch an invisible mouse, which is constrained to moving along the vertices of the graph. Our main focus shall be on trees. We prove that $\lceil (1/2)\log_2(n)\rceil$ cats can always catch a mouse on a tree of order $n$ and give a collection of trees where the mouse can avoid being caught by $ (1/4 - o(1))\log_2(n)$ cats.

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### BibTeX entry

@article{Catchingamouseonatree, title = {Catching a mouse on a tree}, abstract = {In this paper we consider a pursuit-evasion game on a graph. A team of cats, which may choose any vertex of the graph at any turn, tries to catch an invisible mouse, which is constrained to moving along the vertices of the graph. Our main focus shall be on trees. We prove that {\$}\lceil (1/2)\log{\_}2(n)\rceil{\$} cats can always catch a mouse on a tree of order {\$}n{\$} and give a collection of trees where the mouse can avoid being caught by {\$} (1/4 - o(1))\log{\_}2(n){\$} cats.}, url = {http://arxiv.org/abs/1502.06591v1 http://arxiv.org/pdf/1502.06591v1}, year = 2015, author = {Vytautas Gruslys and Arès M{\'{e}}roueh}, comment = {}, urldate = {2019-10-08}, archivePrefix = {arXiv}, eprint = {1502.06591}, primaryClass = {math.CO}, collections = {animals,attention-grabbing-titles,combinatorics} }