Parallel 5-colouring of planar graphs

  • Torben Hagerup
  • Marek Chrobak
  • Krzysztof Diks
Parallel And Distributed Computing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


We show that a 5-colouring of the vertices of an n-vertex planar graph may be computed in O(log n log* n) time by an exclusive-read exclusive-write parallel RAM with O(n/(log n log* n)) processors. Our algorithm, while faster than all previously known methods, is at the same time the first parallel 5-colouring algorithm to achieve optimal speedup. It should be emphasized that although input to the algorithm is a planar graph, we do not require a planar embedding to be given as part of the input.

Other results concern the colouring of graphs of bounded genus and the construction of search structures for triangular planar subdivisions.


Planar Graph Search Structure Adjacency List Vertex Number Planar Embedding 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Torben Hagerup
    • 1
  • Marek Chrobak
    • 2
  • Krzysztof Diks
    • 3
  1. 1.Fachbereich InformatikUniversität des SaarlandesSaarbrückenWest Germany
  2. 2.Department of Computer ScienceColumbia UniversityNew YorkUSA
  3. 3.Institute of InformaticsWarsaw University, PKiN VIIIp.WarsawPoland

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