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The Fast Search Number of a Complete k-Partite Graph

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Abstract

Research on graph searching has recently gained interest in computer science, mathematics, and physics. This paper studies fast searching of a fugitive in a graph, a model that was introduced by Dyer et al. (in: Fleischer, Xu (eds.) Algorithmic aspects in information and management, Springer, New York, 2008). We provide lower bounds and upper bounds on the fast search number (i.e., the minimum number of searchers required for capturing the fugitive) of complete k-partite graphs. We also investigate some special classes of complete k-partite graphs, such as complete bipartite graphs and complete split graphs. We solve the open problem of determining the fast search number of complete bipartite graphs, and present upper and lower bounds on the fast search number of complete split graphs.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions, which improved the presentation of this paper.

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Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S0A2, Canada

    Yuan Xue, Boting Yang & Sandra Zilles

  2. College of Math, Physics and Information Technology, Zhejiang Normal University, Jinhua, Zhejiang, China

    Farong Zhong

Authors
  1. Yuan Xue
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  2. Boting Yang
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  3. Farong Zhong
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  4. Sandra Zilles
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Corresponding author

Correspondence to Boting Yang.

Additional information

B. Yang: Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2013-261290.

F. Zhong: Research supported in part by Department of Science and Technology of Zhejiang Province, China, Application No: 2015C33085.

S. Zilles: Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2017-05336.

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Xue, Y., Yang, B., Zhong, F. et al. The Fast Search Number of a Complete k-Partite Graph. Algorithmica 80, 3959–3981 (2018). https://doi.org/10.1007/s00453-018-0456-z

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  • DOI: https://doi.org/10.1007/s00453-018-0456-z

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