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Minus Domination in Small-Degree Graphs

(Extended abstract)
  • Peter Damaschke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

Abstract

Minus domination in graphs is a variant of domination where the vertices must be labeled -1,0,+1 such that the sum of labels in each N[v] is positive. (As usual, N[v] means the set containing v together with its neighbors.) The minus domination number γ is the minimum total sum of labels that can be achieved. In this paper we prove linear lower bounds for γ in graphs either with Δ ≤ 3, or with Δ ≤ 4 but without vertices of degree 2. The central section is concerned with complexity results for Δ ≤ 4: We show that computing γ is NP-hard and MAX SNP-hard there, but that γ can be approximated in linear time within some constant factor. Finally, our approach also applies to signed domination (where the labels are -1,+1 only) in small-degree graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Peter Damaschke
    • 1
  1. 1.Theoretische Informatik IIFernUniversitätHagenGermany

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