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- W2783253555 abstract "In this paper, we study covering and domination problems on directed graphs.Although undirected Vertex Cover and Edge Dominating Set are well-studied classical graph problems, the directed versions have not been studied much due to the lack of clear definitions.We give natural definitions for Directed r-In (Out) Vertex Cover and Directed (p,q)-Edge Dominating Set as directed generations of Vertex Cover and Edge Dominating Set.For these problems, we show that(1) Directed r-In (Out) Vertex Cover and Directed (p,q)-Edge Dominating Set are NP-complete on planar directed acyclic graphs except when r=1 or (p,q)=(0,0),(2) if r>=2, Directed r-In (Out) Vertex Cover is W[2]-hard and (c*ln k)-inapproximable on directed acyclic graphs,(3) if either p or q is greater than 1, Directed (p,q)-Edge Dominating Set is W[2]-hard and (c*ln k)-inapproximable on directed acyclic graphs,(4) all problems can be solved in polynomial time on trees, and(5) Directed (0,1),(1,0),(1,1)-Edge Dominating Set are fixed-parameter tractable in general graphs.The first result implies that (directed) r-Dominating Set on directed line graphs is NP-complete even if r=1." @default.
- W2783253555 created "2018-01-26" @default.
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- W2783253555 date "2017-01-01" @default.
- W2783253555 modified "2023-09-23" @default.
- W2783253555 title "On Directed Covering and Domination Problems" @default.
- W2783253555 doi "https://doi.org/10.4230/lipics.isaac.2017.45" @default.
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