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<p>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.</p>

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Surrounding an Active Robber

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Nancy E. Clarke,
  • Stephen Finbow,
  • Todd Mullen

摘要

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.