Skip to main content
SpringerLink
Log in

On Complexity of Total Vertex Cover on Subcubic Graphs

  • Conference paper
  • First Online:
Book cover Theory and Applications of Models of Computation (TAMC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10185))

  • 808 Accesses

Abstract

A total vertex cover is a vertex cover whose induced subgraph consists of a set of connected components, each of which contains at least two vertices. A t-total vertex cover is a total vertex cover where each component of its induced subgraph contains at least t vertices. The total vertex cover (TVC) problem and the t-total vertex cover (t-TVC) problem ask for the corresponding cover set with minimum cardinality, respectively. In this paper, we first show that the t-TVC problem is NP-complete for connected subcubic grid graphs of arbitrarily large girth. Next, we show that the t-TVC problem is NP-complete for 3-connected cubic planar graphs. Moreover, we show that the t-TVC problem is APX-complete for connected subcubic graphs of arbitrarily large girth.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoret. Comput. Sci. 237(1–2), 123–134 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Crescenzi, P.: A short guide to approximation preserving reductions. In: Proceedings of the 12th Annual IEEE Conference on Computational Complexity, pp. 262–273 (1997)

    Google Scholar 

  3. de Berg, M., Khosravi, A.: Optimal binary space partitions in the plane. In: Proceedings of the 16th International Conference on Computing and Combinatorics, pp. 329–343 (2010)

    Google Scholar 

  4. Fernau, H., Manlove, D.F.: Vertex and edge covers with clustering properties: complexity and algorithms. J. Discrete Algorithms 7(2), 149–167 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Garey, M.R., Johnson, D.S.: The rectilinear steiner tree problem is NP-complete. SIAM J. Appl. Math. 32(4), 826–834 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  6. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)

    Google Scholar 

  7. Gross, J.L., Yellen, J.: Graph Theory and Its Applications. CRC Press, Boca Raton (2005)

    Google Scholar 

  8. Hopcroft, J.E., Karp, R.M.: A \(n^{5/2}\) algorithm for maximum matchings in bipartite. In: Proceedings of 12th Annual IEEE Symposium on Switching and Automata Theory, pp. 225–231 (1971)

    Google Scholar 

  9. Karp, R.M.: Reducibility among combinatorial problems. In: Proceedings of a Symposium on the Complexity of Computer Computations, pp. 85–103 (1972)

    Google Scholar 

  10. König, D.: Vgráfok és mátrixok. Matematikai és Fizikai Lapok 38, 116–119 (1931)

    Google Scholar 

  11. Murphy, O.J.: Computing independent sets in graphs with large girth. Discrete Appl. Math. 35(2), 167–170 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Uehara, R.: NP-complete problems on a 3-connected cubic planar graph and their applications. Technical Report TWCU-M-0004, Tokyo Woman’s Christian University (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing and Informatics, Universiti Teknologi Brunei, Gadong, Brunei Darussalam

    Sheung-Hung Poon

  2. Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan

    Wei-Lin Wang

  3. Institute of Information Systems and Applications, National Tsing Hua University, Hsinchu, Taiwan

    Wei-Lin Wang

Authors
  1. Sheung-Hung Poon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei-Lin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sheung-Hung Poon .

Editor information

Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Poon, SH., Wang, WL. (2017). On Complexity of Total Vertex Cover on Subcubic Graphs. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-55911-7_37

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55910-0

  • Online ISBN: 978-3-319-55911-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation