On the performance guarantee of First Fit for sum coloring

Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


In sum coloring, it is required to find a proper coloring of the vertices of a graph using positive integers, such that the sum of colors of the vertices is minimized. First Fit is the natural coloring algorithm that processes vertices one by one (in some order), and colors the current vertex with the minimum color that was not used for any of its already considered neighbors. Here, we study the approximation ratio of First Fit for sum coloring for the class of claw-free graphs, its most natural subclasses, and its generalizations, and get tight bounds for it.

Original languageEnglish
Pages (from-to)91-105
Number of pages15
JournalJournal of Computer and System Sciences
StatePublished - Feb 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.


  • Approximation algorithm
  • Chromatic sum number of graphs
  • First Fit
  • Graph coloring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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