A linear time algorithm to compute a minimum restrained dominating set in proper interval graphs
2015 ◽
Vol 07
(02)
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pp. 1550020
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Keyword(s):
A set D ⊆ V is a restrained dominating set of a graph G = (V, E) if every vertex in V\D is adjacent to a vertex in D and a vertex in V\D. Given a graph G and a positive integer k, the restrained domination problem is to check whether G has a restrained dominating set of size at most k. The restrained domination problem is known to be NP-complete even for chordal graphs. In this paper, we propose a linear time algorithm to compute a minimum restrained dominating set of a proper interval graph. We present a polynomial time reduction that proves the NP-completeness of the restrained domination problem for undirected path graphs, chordal bipartite graphs, circle graphs, and planar graphs.
1995 ◽
Vol 56
(3)
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pp. 179-184
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Keyword(s):
2009 ◽
Vol 110
(1)
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pp. 20-23
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Keyword(s):
2021 ◽
Vol vol. 23 no. 1
(Discrete Algorithms)
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Keyword(s):
2011 ◽
Vol 50
(4)
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pp. 721-738
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Keyword(s):
1992 ◽
Vol 43
(6)
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pp. 297-300
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Keyword(s):
Keyword(s):
2013 ◽
Vol 113
(19-21)
◽
pp. 815-822
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Keyword(s):