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Cops and robbers in graphs with large girth and Cayley graphs

https://doi.org/10.1016/0166-218X(87)90033-3Get rights and content
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Abstract

It is shown that if a graph has girth at least 8t−3 and minimum degree greater that d, then more than dt cops are needed to catch a robber. Some upper bounds, in particular for Cayley graphs of groups, are also obtained.

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