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× m)-grid is minn,m/2+1. We also show that the extremal value of this number on n-vertex trees is between (log n/log log n) and O(log n).
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