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On the parameterized vertex cover problem for graphs with perfect matching

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Abstract

A vertex cover of an n-vertex graph with perfect matching contains at least n/2 vertices. In this paper, we study the parameterized complexity of the problem vc-pm* that decides if a given graph with perfect matching has a vertex cover of size bounded by n/2 +k. We first present an algorithm of running time O*(4k) for a variation of the vertex cover problem on König graphs with perfect matching. This algorithm combined with the iterative compression technique leads to an algorithm of running time O*(9k) for the problem vc-pm*. Our result improves the previous best algorithm of running time O*(15k) for the vc-pm* problem, which reduces the problem to the almost 2-sat problem and solves the latter by Razgon and O’Sullivan’s recent algorithm.

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    JianXin Wang, WenJun Li, ShaoHua Li & JianEr Chen

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, Texas, 77843-3112, USA

    JianEr Chen

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  1. JianXin Wang
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  2. WenJun Li
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  3. ShaoHua Li
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  4. JianEr Chen
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Correspondence to JianXin Wang.

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Wang, J., Li, W., Li, S. et al. On the parameterized vertex cover problem for graphs with perfect matching. Sci. China Inf. Sci. 57, 1–12 (2014). https://doi.org/10.1007/s11432-013-4845-2

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  • DOI: https://doi.org/10.1007/s11432-013-4845-2

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