More Lower Bounds for Weak Sense of Direction: The Case of Regular Graphs

  • Paolo Boldi
  • Sebastiano Vigna‡
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1914)


A graph G with n vertices and maximum degree δG cannot be given weak sense of direction using less than δG colours. It is known that n colours are always sufficient, and it was conjectured that just δG + 1 are really needed, that is, one more colour is sufficient. Nonetheless, it has just been shown [2] that for sufficiently large n there are graphs requiring Ω(n/log n) more colours than δG. In this paper, using recent results in asymptotic graph enumeration, we show not only that (somehow surprisingly) the same bound holds for regular graphs, but also that it can be improved to Ω(n log log n/ log n). We also show that Ω (dG√log log dG) colours are necessary, where dG is the degree of G.


Random Graph Regular Graph Weak Sense Additional Colour Local Naming 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Paolo Boldi
    • 1
  • Sebastiano Vigna‡
    • 1
  1. 1.Dipartimento di Scienze deH’InformazioneUniversità degli Studi di MilanoItaly

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