Complexity of Cycle Transverse Matching Problems

  • Ross Churchley
  • Jing Huang
  • Xuding Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)

Abstract

The stable transversal problem for a fixed graph H asks whether a graph contains a stable set that meets every induced copy of H in the graph. Stable transversal problems generalize several vertex partition problems and have been studied for various classes of graphs. Following a result of Farrugia, the stable transversal problem for each C with ℓ ≥ 3 is NP-complete. In this paper, we study an ‘edge version’ of these problems. Specifically, we investigate the problem of determining whether a graph contains a matching that meets every copy of H. We show that the problem for C3 is polynomial and for each C with ℓ ≥ 4 is NP-complete. Our results imply that the stable transversal problem for each C with ℓ ≥ 4 remains NP-complete when it is restricted to line graphs. We show by contrast that the stable transversal problem for C3, when restricted to line graphs, is polynomial.

Keywords

Stable transversal problem transverse matching problem algorithm complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ross Churchley
    • 1
  • Jing Huang
    • 1
  • Xuding Zhu
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  2. 2.Department of mathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China

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