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Abstract
Given a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and is denoted by ρk (G). It is well known that γpr(G) ≤ 2γ (G). In this paper, we prove that it is NP-hard to determine whether γpr(G) = 2γ (G) even for bipartite graphs. We provide a simple characterization of trees with γpr(G) = 2γ (G), implying a polynomial-time recognition algorithm. We also prove that even for a bipartite graph, it is NP-hard to determine whether γpr(G) = γt(G). We finally prove that it is both NP-hard to determine whether γpr(G) = 2ρ4(G) and whether γpr(G) = 2ρ3(G).
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Authors (3)
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Didem Gözüpek
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Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10878-022-00873-y
- License
- Copyright (2022 Springer Science+Business Media, LLC, part of Springer Nature)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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JOURNAL OF COMBINATORIAL OPTIMIZATION
no. 44,
pages 921 - 933,
ISSN: 1382-6905 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Dettlaff M., Gözüpek D., Raczek J.: Paired domination versus domination and packing number in graphs// JOURNAL OF COMBINATORIAL OPTIMIZATION -Vol. 44,iss. 2 (2022), s.921-933
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10878-022-00873-y
- Verified by:
- Gdańsk University of Technology
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