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Complexity of Cycle Transverse Matching Problems

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Combinatorial Algorithms (IWOCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7056))

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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 ℓ 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 ℓ with ℓ ≥ 4 is NP-complete. Our results imply that the stable transversal problem for each C ℓ 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.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada, V8W 3R4

    Ross Churchley & Jing Huang

  2. Department of mathematics, Zhejiang Normal University, Jinhua, Zhejiang, People’s Republic of China

    Xuding Zhu

Authors
  1. Ross Churchley
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  2. Jing Huang
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  3. Xuding Zhu
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Editor information

Editors and Affiliations

  1. Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, Australia

    Costas S. Iliopoulos

  2. Department of Computing and Software Information Technology Building, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    William F. Smyth

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© 2011 Springer-Verlag Berlin Heidelberg

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Churchley, R., Huang, J., Zhu, X. (2011). Complexity of Cycle Transverse Matching Problems. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-25011-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25010-1

  • Online ISBN: 978-3-642-25011-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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