How to Hunt an Invisible Rabbit on a Graph
Combinatorics
2015-02-23 v2 Discrete Mathematics
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).
Cite
@article{arxiv.1502.05614,
title = {How to Hunt an Invisible Rabbit on a Graph},
author = {Tatjana V. Abramovskaya and Fedor V. Fomin and Petr A. Golovach and Michał Pilipczuk},
journal= {arXiv preprint arXiv:1502.05614},
year = {2015}
}