Abstract
We study the entanglement game, which is a version of cops and robbers, on sparse graphs. While the minimum degree of a graph G is a lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops can be much larger, even for graphs with small maximum degree. In particular, we show that there are 3-regular graphs where a linear number of cops are needed.
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Acknowledgments
We thank Malte Milatz for bringing this problem to our attention.
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Martinsson, A., Meier, F., Schnider, P., Steger, A. (2018). Even Flying Cops Should Think Ahead. In: Lee, J., Rinaldi, G., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science(), vol 10856. Springer, Cham. https://doi.org/10.1007/978-3-319-96151-4_28
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DOI: https://doi.org/10.1007/978-3-319-96151-4_28
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