English

Hunter & Mole

Combinatorics 2014-05-15 v2

Abstract

We consider a variation of a cops and robbers game in which the cop---here referred to as "hunter"---is not constrained by the graph but must play in the dark against a "mole." We characterize the graphs---which we will call "hunter-win"---on which the hunter can guarantee capture of the mole in bounded time. We also define an optimal hunter strategy (and consequently an upper bound on maximum game time on hunter-win graphs) and note that an optimal hunter strategy need not take advantage of the hunter's unconstrained movement! This game comes from a puzzle of unknown origin which was told to the authors by Dick Hess.

Keywords

Cite

@article{arxiv.1311.0211,
  title  = {Hunter & Mole},
  author = {Natasha Komarov and Peter Winkler},
  journal= {arXiv preprint arXiv:1311.0211},
  year   = {2014}
}

Comments

This paper has been withdrawn because authors learned that it overlaps significantly with pre-existing work

R2 v1 2026-06-22T01:59:12.270Z