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Four Colouring the Vertices of the Triangulation of a Polygon Containing a Hole

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

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Abstract

A simple linear-time algorithm is presented for four-colouring the vertices of a triangulation of a polygon containing a single hole. The algorithm consists of reducing a triangulation by the removal of both polygon and hole ear vertices, if any, followed by the removal of colour-isolated vertices until a 3-coloured tessellation remains. The triangulation is then re-built, using at most four colours. The paper concludes by recognising the similarity between the colouring of triangulations of polygons containing a hole and the colouring of bipartite and permutation graphs.

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References

  1. O’Rourke, J.: Computational Geometry in C, Cambridge University Press. Cambridge (1994)

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Author information

Authors and Affiliations

  1. School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland

    Graham M. Seed, Raffaella Ocone & Xiaoyan Y. Yang

  2. School of Mathematical and Computing Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland

    Douglas E. R. Clark

Authors
  1. Graham M. Seed
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  2. Douglas E. R. Clark
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  3. Raffaella Ocone
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  4. Xiaoyan Y. Yang
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Seed, G.M., Clark, D.E.R., Ocone, R., Yang, X.Y. (2003). Four Colouring the Vertices of the Triangulation of a Polygon Containing a Hole. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_91

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  • DOI: https://doi.org/10.1007/3-540-44842-X_91

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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