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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Damaschke, P. (1998). Minus Domination in Small-Degree Graphs. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_2
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DOI: https://doi.org/10.1007/10692760_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65195-6
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