Small Connected Planar Graph with 1-Cop-Move Number 4
Discrete Mathematics
2019-12-17 v1 Combinatorics
Abstract
This paper describes a 720-vertex connected planar graph G such that cop1(G), denoting the minimum number of cops needed to catch the robber in the 1-cop-move game on G, is at least 4 and at most 7. Furthermore, G has a connected subgraph H such that cop1(H) is exactly 4, meaning that 4 cops are barely sufficient to catch the robber in the 1-cop-move game on H. This is a significant improvement over the graph given by Gao and Yang in 2017.
Cite
@article{arxiv.1912.07004,
title = {Small Connected Planar Graph with 1-Cop-Move Number 4},
author = {Wei Quan Lim},
journal= {arXiv preprint arXiv:1912.07004},
year = {2019}
}