# 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).

## Other information

key
HowtoHuntanInvisibleRabbitonaGraph
type
article
2019-10-08
date_published
2015-02-02

### BibTeX entry

@article{HowtoHuntanInvisibleRabbitonaGraph,
key = {HowtoHuntanInvisibleRabbitonaGraph},
type = {article},
title = {How to Hunt an Invisible Rabbit on a Graph},
author = {Tatjana V. Abramovskaya and Fedor V. Fomin and Petr A. Golovach and Micha{\l} Pilipczuk},
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).},
comment = {},
}