Coloring the cliques of line graphs

Gábor Bacsó, Zdeněk Ryjáček, Z. Tuza

Research output: Contribution to journalArticle

2 Citations (Scopus)


The . weak chromatic number, or . clique chromatic number (CCHN) of a graph is the minimum number of colors in a vertex coloring, such that every maximal clique gets at least two colors. The . weak chromatic index, or . clique chromatic index (CCHI) of a graph is the CCHN of its line graph.Most of the results here are upper bounds for the CCHI, as functions of some other graph parameters, and contrasting with lower bounds in some cases. Algorithmic aspects are also discussed; the main result within this scope (and in the paper) shows that testing whether the CCHI of a graph equals . 2 is NP-complete. We deal with the CCHN of the graph itself as well.

Original languageEnglish
JournalDiscrete Mathematics
Publication statusAccepted/In press - Apr 4 2016



  • Chromatic number
  • Clique chromatic index
  • Clique chromatic number
  • Line graph
  • Ramsey theory
  • Weak coloring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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