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On the Power of Color Refinement

  • V. Arvind
  • Johannes KöblerEmail author
  • Gaurav Rattan
  • Oleg Verbitsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9210)

Abstract

Color refinement is a classical technique used to show that two given graphs G and H are non-isomorphic; it is very efficient, although it does not succeed on all graphs. We call a graph G amenable to color refinement if the color-refinement procedure succeeds in distinguishing G from any non-isomorphic graph H. Babai, Erdős, and Selkow (1982) have shown that random graphs are amenable with high probability. We determine the exact range of applicability of color refinement by showing that amenable graphs are recognizable in time \(O((n+m)\log n)\), where n and m denote the number of vertices and the number of edges in the input graph.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • V. Arvind
    • 1
  • Johannes Köbler
    • 2
    Email author
  • Gaurav Rattan
    • 1
  • Oleg Verbitsky
    • 2
    • 3
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Institut für InformatikHumboldt Universität zu BerlinBerlinGermany
  3. 3.On leave from the Institute for Applied Problems of Mechanics and MathematicsLvivUkraine

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