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Fast searching games on graphs

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Abstract

Given a graph, suppose that intruders hide on vertices or along edges of the graph. The fast searching problem is to find the minimum number of searchers required to capture all the intruders satisfying the constraint that every edge is traversed exactly once and searchers are not allowed to jump. In this paper, we prove lower bounds on the fast search number. We present a linear time algorithm to compute the fast search number of Halin graphs and their extensions. We present a quadratic time algorithm to compute the fast search number of cubic graphs.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Regina, Regina, Canada

    Donald Stanley

  2. Department of Computer Science, University of Regina, Regina, Canada

    Boting Yang

Authors
  1. Donald Stanley
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  2. Boting Yang
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Corresponding author

Correspondence to Boting Yang.

Additional information

Research of D. Stanley was supported in part by NSERC.

Research of B. Yang was supported in part by NSERC.

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Stanley, D., Yang, B. Fast searching games on graphs. J Comb Optim 22, 763–777 (2011). https://doi.org/10.1007/s10878-010-9328-4

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  • DOI: https://doi.org/10.1007/s10878-010-9328-4

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