Hunting Rabbits on the Hypercube

Abstract

We explore the Hunters and Rabbits game on the hypercube. In the process, we find the solution for all classes of graphs with an isoperimetric nesting property and find the exact hunter number of $Q^n$ to be $1+\sum _{i=0}^{n-2}\left(\genfrac{}{}{0ex}{}{i}{\lfloor i/2\rfloor }\right)$. In addition, we extend results to the situation where we allow the rabbit to not move between shots.

17 pages, to appear in Discrete Mathematics