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Properly Coloured Cycles and Paths: Results and Open Problems

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Graph Theory, Computational Intelligence and Thought

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5420))

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Abstract

In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prove new ones. In particular, we consider a family of transformations of an edge-coloured multigraph G into an ordinary graph that allow us to check the existence of PC cycles and PC (s,t)-paths in G and, if they exist, to find shortest ones among them. We raise a problem of finding the optimal transformation and consider a possible solution to the problem.

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Authors and Affiliations

  1. Department of Computer Science, University of London, Egham, Royal Holloway, Surrey, TW20 0EX, UK

    Gregory Gutin & Eun Jung Kim

Authors
  1. Gregory Gutin
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  2. Eun Jung Kim
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Editor information

Editors and Affiliations

  1. The Caesarea Rothschild Institute, Mount Carmel, University of Haifa, 31905, Haifa, Israel

    Marina Lipshteyn

  2. Department of Computer Science and Mathematics, Ariel University Center of Samaria, 40700, Ariel, Israel

    Vadim E. Levit

  3. Department of Computer Science, Colorado State University, 80523-1873, Fort Collins, CO, USA

    Ross M. McConnell

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Gutin, G., Jung Kim, E. (2009). Properly Coloured Cycles and Paths: Results and Open Problems. In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds) Graph Theory, Computational Intelligence and Thought. Lecture Notes in Computer Science, vol 5420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02029-2_19

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  • DOI: https://doi.org/10.1007/978-3-642-02029-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02028-5

  • Online ISBN: 978-3-642-02029-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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