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I am considering to investigate on a variation of the cops and robber game where the robber is considered as an "invisible evader" for their location is unknown until one of the cops are at an adjacent node to the robber.

I was just wondering whether this has been previously studied by any individuals and if so, how much. It would be really helpful if I can be directed to that study.

Thank you.

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    $\begingroup$ It's not clear to me why this question has so many downvotes. $\endgroup$
    – Ben Barber
    Dec 3, 2017 at 17:41

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A variation where the robber is invisible until at distance $\ell$ of some cop for a fixed parameter $\ell$ is considered in the preprint Limited Visibility Cops and Robbers. The version you suggest is $\ell = 1$, and the preprint cites the following master's thesis as a source for the $\ell=1$ case:

A. Tang, Cops and robber with bounded visibility, Master’s thesis, Dalhousie University, 2004.

I was unable to find this master thesis through a quick google search. Some other references within the preprint may also be of interest to you.

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