Surrounding an Active Robber

doi:10.1007/s44007-026-00206-z

Surrounding an Active Robber

2026-04-04

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DOI：10.1007/s44007-026-00206-z

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We look at an active version of Surrounding Cops and Robber in which the robber must never remain on their current vertex. Our parameter of interest is the active surrounding number of a graph: the minimum number of cops that suffice to surround the robber on that graph. We find exact values of our parameter for some graph families, establish bounds for others, and also explore some particular graph families for which the active surrounding number differs from the analogous parameters for several related variants.

Keywords:

Pursuit-evasion on graphs

Cops and Robber

Copnumber

Surrounding copnumber

Games on graphs

Surrounding an Active Robber

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