Pursuit-Evasion in a Two-Dimensional Domain
Published in Ars Mathematica Contemporanea, 2017
A. Beveridge, Y. Cai, Pursuit-Evasion in a Two-Dimensional Domain, Ars Mathematica Contemporanea, Vol. 13 (2017), 187-206.
Preprint link: https://arxiv.org/abs/1505.00297
We prove two general results about pursuit-evasion games in topological space, where the pursuer must obtain colocation to achieve capture. Firstly, one pursuer has a winning strategy in any CAT(0) space. Secondly, three pursuers hava a winning strategy in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic.