Improper C-colorings of graphs

Csilla Bujtás, E. Sampathkumar, Zsolt Tuza, L. Pushpalatha, R. C. Vasundhara

Research output: Contribution to journalArticle

5 Citations (Scopus)


For an integer k≥1, the k-improper upper chromatic number χ̄k-imp(G) of a graph G is introduced here as the maximum number of colors permitted to color the vertices of G such that, for any vertex ν in G, at most k vertices in the neighborhood N(ν) of ν receive colors different from that of ν. The exact value of χ̄k-impis determined for several types of graphs, and general estimates are given in terms of various graph invariants, e.g. minimum and maximum degree, vertex covering number, domination number and neighborhood number. Along with bounds on χ̄k-imp for Cartesian products of graphs, exact results are found for hypercubes. Also, the analogue of the NordhausGaddum theorem is proved. Moreover, the algorithmic complexity of determining χ̄ k-imp is studied, and structural correspondence between k-improper C-colorings and certain kinds of edge cuts is shown.

Original languageEnglish
Pages (from-to)174-186
Number of pages13
JournalDiscrete Applied Mathematics
Issue number4
Publication statusPublished - Feb 28 2011


  • 3-consecutive coloring
  • Edge cut
  • Graph improper coloring
  • Upper chromatic number
  • k-improper C-coloring

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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  • Cite this

    Bujtás, C., Sampathkumar, E., Tuza, Z., Pushpalatha, L., & Vasundhara, R. C. (2011). Improper C-colorings of graphs. Discrete Applied Mathematics, 159(4), 174-186.