Eternally surrounding a robber
Combinatorics
2025-08-15 v3
Abstract
We introduce the bodyguard problem for graphs. This is a variation of Surrounding Cops and Robber but, in this model, a smallest possible group of bodyguards must surround the president and then maintain this protection indefinitely. We investigate some elementary bounds, then solve this problem for the infinite graph families of complete graphs, wheels, trees, cycles, complete multipartite graphs, and two-dimensional grids. We also examine the problem in more general Cartesian, strong, and lexicographic products.
Cite
@article{arxiv.2408.10452,
title = {Eternally surrounding a robber},
author = {Nancy E. Clarke and Danny Dyer and William Kellough},
journal= {arXiv preprint arXiv:2408.10452},
year = {2025}
}
Comments
26 pages, 3 figures