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arXiv · 1912.07004

Small Connected Planar Graph with 1-Cop-Move Number 4

Wei Quan Lim
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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.

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Wei Quan Lim. 2019-12-15. Small Connected Planar Graph with 1-Cop-Move Number 4. https://arxiv.org/abs/1912.07004

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