Guarding isometric subgraphs and Cops and Robber in planar graphs
<|reference_start|>Guarding isometric subgraphs and Cops and Robber in planar graphs: In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shadow in a subgraph, and use it to characterize all 1-guardable graphs. As an application, we show that 3 cops can capture a robber in any planar graph with the added restriction that at most two cops can move simultaneously, proving a conjecture of Yang and strengthening a classical result of Aigner and Fromme.<|reference_end|>
@article{de la maza2024guarding,
    title={Guarding isometric subgraphs and Cops and Robber in planar graphs},
    author={Sebasti'an Gonz'alez Hermosillo de la Maza and Bojan Mohar},
    journal={Europ. J. Combin. 119 (2024) 103809},
    year={2024},
    doi={10.1016/j.ejc.2023.103809},
    archivePrefix={arXiv},
    eprint={2406.01068},
    primaryClass={math.CO cs.DM}
}