Generalized domination in chordal graphs

  • Authors:

  • Jan Kratochvíl;Paul D. Manuel;Mirka Miller

  • Affiliations:

  • Charles University, Prague, KAM MFF UK, Malostranské nám. 25, 110 00 Praha 1, Czech Republic;Department of Computer Science, University of Newcastle, Newcastle, Australia;Department of Computer Science, University of Newcastle, Newcastle, Australia

  • Venue:
  • Nordic Journal of Computing
  • Year:
  • 1995

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Abstract

We discuss the computational complexity of generalized domination problems, which were introduced in [J.A.Telle: Complexity of domination-type problems in graphs, Nordic Journal of Computing 1 (1994), 157-171], restricted to chordal and interval graphs. The existence problem, parametrized by two sets of nonnegative integers σ and ρ, asks for the existence of a set S of vertices of a given graph such that for every vertex u ∈ S (or u ∉ S), the number of neighbors of u which are in S is in σ (in ρ, respectively). Telle proved that this problem is NP-complete for general graphs, provided both σ and ρ are finite and 0 ∉ ρ. One of our main results shows that in such cases, the existence problem is polynomially solvable for interval graphs. On the other hand, for chordal graphs, the complexity of the existence problem varies significantly even when σ and ρ contain one element each.