# How to Hunt an Invisible Rabbit on a Graph

- Published in 2015
- Added on

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We investigate Hunters & Rabbit game, where a set of hunters tries to catch an invisible rabbit that slides along the edges of a graph. We show that the minimum number of hunters required to win on an (n\times m)-grid is \lfloor min{n,m}/2\rfloor+1. We also show that the extremal value of this number on n-vertex trees is between \Omega(log n/log log n) and O(log n).

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### BibTeX entry

@article{HowtoHuntanInvisibleRabbitonaGraph, title = {How to Hunt an Invisible Rabbit on a Graph}, abstract = {We investigate Hunters {\&} Rabbit game, where a set of hunters tries to catch an invisible rabbit that slides along the edges of a graph. We show that the minimum number of hunters required to win on an (n\times m)-grid is \lfloor min{\{}n,m{\}}/2\rfloor+1. We also show that the extremal value of this number on n-vertex trees is between \Omega(log n/log log n) and O(log n).}, url = {http://arxiv.org/abs/1502.05614v2 http://arxiv.org/pdf/1502.05614v2}, year = 2015, author = {Tatjana V. Abramovskaya and Fedor V. Fomin and Petr A. Golovach and Micha{\l} Pilipczuk}, comment = {}, urldate = {2019-10-08}, archivePrefix = {arXiv}, eprint = {1502.05614}, primaryClass = {math.CO}, collections = {animals,attention-grabbing-titles,combinatorics,easily-explained,protocols-and-strategies,puzzles} }