A new kind of graph coloring

  • Authors:

  • Igor E. Zverovich

  • Affiliations:

  • RUTCOR -- Rutgers Center for Operations Research, Rutgers, The State University of New Jersey, 640 Bartholomew Road, Piscataway, NJ 08854-8003, USA

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2006

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Abstract

A proper k-coloring C^1,C^2,...,C^k of a graph G is called strong if, for every vertex u@?V(G), there exists an index i@?{1,2,...,k} such that u is adjacent to every vertex of C^i. We consider classes SCOLOR(k) of strongly k-colorable graphs and show that the recognition problem of SCOLOR(k) is NP-complete for every k=4, but it is polynomial-time solvable for k=3. We give a characterization of SCOLOR(3) in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring.