Skip to main content
SpringerLink
Log in

On Evasion Games on Graphs

  • Conference paper
  • First Online:
Discrete and Computational Geometry and Graphs (JCDCGG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9943))

Included in the following conference series:

  • 833 Accesses

Abstract

We consider an evasion game on a connected simple graph. We first show that the pursuit number of a graph G, the smallest k such that k pursuers win the game, is bounded above by the pathwidth of G. We next show that the pursuit number of G is two if and only if the pathwidth of G is one. We also show that for any integer \({w}\ge 2\), there exists a tree T such that the pursuit number of T is three and the pathwidth of T is w.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abramovskaya, T.V., Fomin, F.V., Golovach, P.A., Pilipczuk, M.: How to hunt an invisible rabbit on a graph. Eur. J. Comb. 52, 12–26 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  2. Britnell, J.R., Wildon, M.: Finding a princess in a palace: a pursuit evasion problem. Electron. J. Comb. 20, 25 (2013)

    MathSciNet  MATH  Google Scholar 

  3. Gruslys, V., Mèrouéh, A.: Catching a mouse on a tree. arXiv.org/abs/1502.06591 (2015)

  4. Haslegrave, J.: An evasion game on a graph. Discrete Math. 314, 1–5 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Robertson, N., Seymour, P.: Graph minors I. Excluding a forest. J. Comb. Theor. Series B 35, 39–61 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Scheffler, P.: Optimal embedding of a tree into an interval graph in linear time. Ann. Discret. Math. 51, 278–291 (1992)

    MathSciNet  MATH  Google Scholar 

  7. Shrestha, A.M.S., Tayu, S., Ueno, S.: On orthogonal ray graphs. Discrete Appl. Math. 158, 1650–1659 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Takahashi, A., Ueno, S., Kajitani, Y.: Minimal acyclic forbidden minors for the family of graphs with bounded path-width. Discrete Math. 127, 293–304 (1994)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The research was partially supported by JSPS KAKENHI Grant Number 26330007.

Author information

Authors and Affiliations

  1. Department of Information and Communications Engineering, Tokyo Institute of Technology, Tokyo, 152-8550-S3-57, Japan

    Satoshi Tayu & Shuichi Ueno

Authors
  1. Satoshi Tayu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuichi Ueno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Satoshi Tayu .

Editor information

Editors and Affiliations

  1. Tokyo University of Science , Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications , Tokyo, Japan

    Hiro Ito

  3. Tokai University , Tokyo, Japan

    Toshinori Sakai

  4. Osaka Prefecture University , Sakai, Japan

    Yushi Uno

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Tayu, S., Ueno, S. (2016). On Evasion Games on Graphs. In: Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science(), vol 9943. Springer, Cham. https://doi.org/10.1007/978-3-319-48532-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48532-4_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48531-7

  • Online ISBN: 978-3-319-48532-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation