The distant-2 chromatic number of random proximity and random geometric graphs

Josep Díaz, Zvi Lotker, Maria Serna

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We are interested in finding bounds for the distant-2 chromatic number of geometric graphs drawn from different models. We consider two undirected models of random graphs: random geometric graphs and random proximity graphs for which sharp connectivity thresholds have been shown. We are interested in a.a.s. connected graphs close just above the connectivity threshold. For such subfamilies of random graphs we show that the distant-2-chromatic number is Θ (log n) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. Díaz, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143-154].

Original languageEnglish
Pages (from-to)144-148
Number of pages5
JournalInformation Processing Letters
Issue number4
StatePublished - 16 May 2008


  • Coloring
  • Combinatorial problems
  • Distant-2 coloring
  • Graph algorithms
  • Random graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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