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Categorical Perspectives pp 243–263Cite as

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The Copnumber of a Graph is Bounded by [3/2 genus (G)] + 3

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Abstract

We prove that the copnumber of a finite connected graph of genus g is bounded by [3/2g]+3. In particular this means that the copnumber of a toroidal graph is bounded by 4. We also sketch a proof that the copnumber of a graph of genus 2 is bounded by 5.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Andreae. Note on a pursuit game played on graphs, Discrete Appl. Math., 9 (1984), 111–115.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Andreae. On a pursuit game played on a graph for which a minor is excluded, J. Combin. Theory (Ser. B), 41 (1986), 37–47.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Anstee and M. Farber. On bridged graphs and cop-win graphs, J. Combin. Theory (Ser. B), 44 (1988), 22–28.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Berarducci and B. Intrigila. On the copnumber of a graph, Advances in Applied Mathematics, 14 (1993), 389–403.

    Article  MathSciNet  MATH  Google Scholar 

  6. S. Fitzpatrick and R. Nowakowski. The copnumber of graphs with strong isometric dimension 2, preprint (1997).

    Google Scholar 

  7. R Frankl. Cops and robbers in graphs with large girth and Cayley graphs, Discrete Appl. Math., 17 (1987), 301–305.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Goldstein and E. Reingold. The complexity of pursuit on a graph, Theoretical Computer Science, 143 (1995), 93–112.

    MathSciNet  MATH  Google Scholar 

  9. M. W. Hirsch. Differential Topology, Graduate Texts in Mathematics, 33, Springer Verlag, New York, 1976.

    Book  MATH  Google Scholar 

  10. M. Maamoun and H. Meyniel. On a game of policemen and robber, Discrete Appl. Math., 17 (1987), 307–309.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Neufeld and R. Nowakowski. A vertex-to-vertex pursuit game with disjoint sets of edges, in: Sauer, et. al., Finite and Infinite Combinatorics in Sets and Logic, NATO ASI Series C, Vol. 411 (1991), 299–312.

    Google Scholar 

  12. R. Nowakowski, B. Schröder. Bounding the copnumber using the crosscap number, unpublished manuscript, 1998.

    Google Scholar 

  13. R. Nowakowski and P. Winkler. Vertex-to-vertex pursuit in a graph, Discrete Mathematics, 43 (1983), 235–239.

    Article  MathSciNet  MATH  Google Scholar 

  14. N. Polat, Retract-collapsible graphs and invariant subgraph properties, J. Graph Theory, 19, (1995), 25–44.

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Quilliot. Thèse de doctorat d’etat, Université de Paris VI, 1983.

    Google Scholar 

  16. A. Quilliot. A short note about pursuit games played on a graph with a given genus, J. Combin. Theory (Ser. B), 38 (1985), 89–92.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. White and L. Beineke. Topological graph theory, in: Beineke and Wilson, Selected Topics in Graph Theory, Academic Press, London, 1978.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Program of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA

    Bernd S. W. Schröder

Authors
  1. Bernd S. W. Schröder
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Informatik, TU Braunschweig, 38023, Braunschweig, Germany

    Jürgen Koslowski

  2. Department of Mathematics and Computer Science, Kent State University, Kent, OH, 44242, USA

    Austin Melton

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© 2001 Springer Science+Business Media New York

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Schröder, B.S.W. (2001). The Copnumber of a Graph is Bounded by [3/2 genus (G)] + 3. In: Koslowski, J., Melton, A. (eds) Categorical Perspectives. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1370-3_14

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  • DOI: https://doi.org/10.1007/978-1-4612-1370-3_14

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7117-8

  • Online ISBN: 978-1-4612-1370-3

  • eBook Packages: Springer Book Archive

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