Combinatorica

, Volume 15, Issue 2, pp 255–280 | Cite as

The local nature of Δ-coloring and its algorithmic applications

  • Alessandro Panconesi
  • Aravind Srinivasan
Article

Abstract

Given a connected graphG=(V, E) with |V|=n and maximum degree Δ such thatG is neither a complete graph nor an odd cycle, Brooks' theorem states thatG can be colored with Δ colors. We generalize this as follows: letG-v be Δ-colored; then,v can be colored by considering the vertices in anO(logΔn) radius aroundv and by recoloring anO(logΔn) length “augmenting path” inside it. Using this, we show that Δ-coloringG is reducible inO(log3n/logΔ) time to (Δ+1)-vertex coloringG in a distributed model of computation. This leads to fast distributed algorithms and a linear-processorNC algorithm for Δ-coloring.

Mathematics Subject Classification (1991)

68 Q 22 05 C 15 68 R 10 

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Alessandro Panconesi
    • 1
  • Aravind Srinivasan
    • 2
  1. 1.Fachbereich für Mathematik und Informatik Institut für InformatikFreie Universität BerlinBerlinGermany
  2. 2.DIMACS CenterRutgers UniversityPiscatawayUSA

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