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New Results on the Zero-Visibility Cops and Robber Game

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Algorithmic Aspects in Information and Management (AAIM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11640))

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Abstract

We study the zero-visibility cops and robber game, a variant of the cops and robber game in which the robber is invisible. We give a method for proving lower bounds on the zero-visibility cop number. Using this method, we investigate graph joins, lexicographic products of graphs, complete multipartite graphs and split graphs. Lower bounds and upper bounds, along with rigorous proofs, are given for the zero-visibility cop number of each of these types of graphs.

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References

  1. Aigner, M., Fromme, M.: A game of cops and robbers. Discrete Appl. Math. 8(1), 1–12 (1984)

    Article  MathSciNet  Google Scholar 

  2. Bonato, A.: Conjectures on cops and robbers. In: Gera, R., Hedetniemi, S., Larson, C. (eds.) Graph Theory. PBM, pp. 31–42. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-31940-7_3

    Chapter  Google Scholar 

  3. Bonato, A., Gordinowicz, P., Hahn, G.: Cops and robbers ordinals of cop-win trees. Discrete Math. 340(5), 951–956 (2017)

    Article  MathSciNet  Google Scholar 

  4. Bonato, A., MacGillivray, G.: Characterizations and algorithms for generalized cops and robbers games. Contrib. Discrete Math. 12(1), 110–122 (2017)

    MathSciNet  MATH  Google Scholar 

  5. Bonato, A., Nowakowski, R.: The Game of Cops and Robbers on Graphs. American Mathematical Society, Providence (2011)

    Book  Google Scholar 

  6. Dereniowski, D., Dyer, D., Tifenbach, R.M., Yang, B.: The complexity of zero-visibility cops and robber. Theoret. Comput. Sci. 607, 135–148 (2015)

    Article  MathSciNet  Google Scholar 

  7. Dereniowski, D., Dyer, D., Tifenbach, R.M., Yang, B.: Zero-visibility cops and robber and the pathwidth of a graph. J. Comb. Optim. 29(3), 541–564 (2015)

    Article  MathSciNet  Google Scholar 

  8. Fitzpatrick, S.L., Larkin, J.P.: The game of cops and robber on circulant graphs. Discrete Appl. Math. 225, 64–73 (2017)

    Article  MathSciNet  Google Scholar 

  9. Jeliazkova, D.: Aspects of the cops and robber game played with incomplete information. Master’s thesis, Acadia University (2006)

    Google Scholar 

  10. Kinnersley, W.B.: Cops and robbers is exptime-complete. J. Comb. Theory Ser. B 111, 201–220 (2015)

    Article  MathSciNet  Google Scholar 

  11. Mamino, M.: On the computational complexity of a game of cops and robbers. Theoret. Comput. Sci. 477, 48–56 (2013)

    Article  MathSciNet  Google Scholar 

  12. Nowakowski, R., Winkler, P.: Vertex-to-vertex pursuit in a graph. Discrete Math. 43(2–3), 235–239 (1983)

    Article  MathSciNet  Google Scholar 

  13. Offner, D., Ojakian, K.: Variations of cops and robber on the hypercube. Australas. J. Comb. 59(2), 229–250 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Quilliot, A.: Jeux et pointes fixes sur les graphes. Ph.D. thesis, Université de Paris VI (1978)

    Google Scholar 

  15. Tang, A.: Cops and robber with bounded visibility. Master’s thesis, Dalhousie University (2004)

    Google Scholar 

  16. Tošić, R.: Vertex-to-vertex search in a graph. Graph Theory (Dubrovnik 1985), pp. 233–237 (1985)

    Google Scholar 

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Author information

Authors and Affiliations

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

    Yuan Xue, Boting Yang & Sandra Zilles

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

Correspondence to Yuan Xue .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Hefei University of Technology, Hefei, China

    Lian Li

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

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Xue, Y., Yang, B., Zilles, S. (2019). New Results on the Zero-Visibility Cops and Robber Game. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_29

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  • DOI: https://doi.org/10.1007/978-3-030-27195-4_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27194-7

  • Online ISBN: 978-3-030-27195-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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