# How to Hunt an Invisible Rabbit on a Graph

• Published in 2015
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).

### 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}
}