Generalized H-Coloring of Graphs

  • Authors:

  • Petter Kristiansen;Jan Arne Telle

  • Affiliations:

  • -;-

  • Venue:
  • ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
  • Year:
  • 2000

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Abstract

For fixed simple graph H and subsets of natural numbers σ and ρ, we introduce (H, σ, ρ)-colorings as generalizations of H-colorings of graphs. An (H, σ, ρ)-coloring of a graph G can be seen as a mapping f : V (G) → V (H), such that the neighbors of any v ∈ V (G) are mapped to the closed neighborhood of f(v), with σ constraining the number of neighbors mapped to f(v), and ρ constraining the number of neighbors mapped to each neighbor of f(v). A traditional H-coloring is in this sense an (H, {0}, {0, 1, ...})-coloring. We initiate the study of how these colorings are related and then focus on the problem of deciding if an input graph G has an (H, {0}, {1, 2, ....})-coloring. This H-COLORDOMINATION problem is shown to be no easier than the H-COVER problem and NP-complete for various infinite classes of graphs.