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

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  • Chunmei Liu

    (Howard University)

  • Yinglei Song

    (University of Maryland Eastern Shore)

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

Suggested Citation

  • Chunmei Liu & Yinglei Song, 2011. "Parameterized complexity and inapproximability of dominating set problem in chordal and near chordal graphs," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 684-698, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9317-7
    DOI: 10.1007/s10878-010-9317-7
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    1. Chunmei Liu & Yinglei Song, 2009. "Parameterized dominating set problem in chordal graphs: complexity and lower bound," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 87-97, July.
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