Parameterized complexity and inapproximability of dominating set problem in chordal and near chordal graphs

Chunmei Liu () and Yinglei Song ()
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Chunmei Liu: Howard University
Yinglei Song: University of Maryland Eastern Shore

Journal of Combinatorial Optimization, 2011, vol. 22, issue 4, No 16, 684-698

Abstract: Abstract In this paper, we study the parameterized complexity of Dominating Set problem in chordal graphs and near chordal graphs. We show the problem is W[2]-hard and cannot be solved in time n o(k) in chordal and s-chordal (s>3) graphs unless W[1]=FPT. In addition, we obtain inapproximability results for computing a minimum dominating set in chordal and near chordal graphs. Our results prove that unless NP=P, the minimum dominating set in a chordal or s-chordal (s>3) graph cannot be approximated within a ratio of $\frac{c}{3}\ln{n}$ in polynomial time, where n is the number of vertices in the graph and 0

Keywords: Chordal graphs; Dominating set; Independent dominating set; Parameterized complexity (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-010-9317-7

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