Combinatorica

, Volume 15, Issue 2, pp 255–280

The local nature of Δ-coloring and its algorithmic applications

Authors

  • Alessandro Panconesi
    • Fachbereich für Mathematik und Informatik Institut für InformatikFreie Universität Berlin
  • Aravind Srinivasan
    • DIMACS CenterRutgers University
Article

DOI: 10.1007/BF01200759

Cite this article as:
Panconesi, A. & Srinivasan, A. Combinatorica (1995) 15: 255. doi:10.1007/BF01200759

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 2205 C 1568 R 10

Copyright information

© Akadémiai Kiadó 1995