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)


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 C 3 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 C 3, when restricted to line graphs, is polynomial.


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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