Hunting Rabbits on the Hypercube

• Published in 2017
• Added on 2017-02-06

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 $1+\sum\limits_{i=0}^{n-2} \binom{i}{\lfloor i/2 \rfloor}$. In addition, we extend results to the situation where we allow the rabbit to not move between shots.

Links

• http://arxiv.org/abs/1701.08726v1
• http://arxiv.org/pdf/1701.08726v1

Other information

BibTeX entry

@article{HuntingRabbitsontheHypercube,
	key = {HuntingRabbitsontheHypercube},
	type = {article},
	title = {Hunting Rabbits on the Hypercube},
	author = {Jessalyn Bolkema and Corbin Groothuis},
	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\limits{\_}{\{}i=0{\}}^{\{}n-2{\}} \binom{\{}i{\}}{\{}\lfloor i/2 \rfloor{\}}{\$}. In addition, we
extend results to the situation where we allow the rabbit to not move between
shots.},
	comment = {},
	date_added = {2017-02-06},
	date_published = {2017-10-09},
	urls = {http://arxiv.org/abs/1701.08726v1,http://arxiv.org/pdf/1701.08726v1},
	collections = {Attention-grabbing titles,Easily explained,Protocols and strategies,Animals,Food},
	url = {http://arxiv.org/abs/1701.08726v1 http://arxiv.org/pdf/1701.08726v1},
	urldate = {2017-02-06},
	archivePrefix = {arXiv},
	eprint = {1701.08726},
	primaryClass = {math.CO},
	year = 2017
}