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Algorithmica

, Volume 80, Issue 12, pp 3959–3981 | Cite as

The Fast Search Number of a Complete k-Partite Graph

  • Yuan Xue
  • Boting Yang
  • Farong Zhong
  • Sandra Zilles
Article
  • 79 Downloads

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.

Keywords

Fast searching Complete k-partite graph Bipartite graph Split graph 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Yuan Xue
    • 1
  • Boting Yang
    • 1
  • Farong Zhong
    • 2
  • Sandra Zilles
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada
  2. 2.College of Math, Physics and Information TechnologyZhejiang Normal UniversityJinhuaChina

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