Skip to main content
SpringerLink
Log in

The lexicographically first maximal subgraph problems: P-completeness and NC algorithms

  • Algorithms And Complexity
  • Conference paper
  • First Online:
Book cover Automata, Languages and Programming (ICALP 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 267))

Included in the following conference series:

Abstract

The P-completeness of the lexicographically first maximal (l.f.m.) subgraph problem for any nontrivial hereditary property is proved. If the instances are restricted to graphs with degree at most 3, the l.f.m. 4-cycle free subgraph problem is shown to be in NC2. This degree constraint 3 is best possible.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Asano and T. Hirata, Edge-deletion and edge-contraction problems, Proc. 14th ACM STOC (1982) 245–254.

    Google Scholar 

  2. S.A. Cook, An observation on time-storage trade off, J. Comput. System Sci. 9 (1974) 308–316.

    Google Scholar 

  3. S.A. Cook, A taxonomy of problems with fast parallel algorithms, Inform. Contr. 64 (1985) 2–22.

    Google Scholar 

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

    Article  Google Scholar 

  5. L.M. Goldschlager, The monotone and planar circuit value problems are log space complete for P, SIGACT News 9 (1977) 25–29.

    Article  Google Scholar 

  6. D.B. Johnson and S.M. Venkatesan, Parallel algorithm for minimum cuts and maximum flows in planar networks, Proc. 22nd IEEE FOCS (1982) 244–254.

    Google Scholar 

  7. R.M. Karp, E. Upfal and A. Wigderson, Constructing a perfect matching is in random NC, Proc. 17th ACM STOC (1985) 22–32.

    Google Scholar 

  8. R.E. Ladner, The circuit value problem is log-space complete for P, SIGACT News 7 (1975) 18–20.

    Article  Google Scholar 

  9. J.M. Lewis and M. Yannakakis, The node deletion problems for hereditary properties is NP-complete, J. Comput. System Sci. 20 (1980) 219–230.

    Google Scholar 

  10. M. Luby, A simple parallel algorithm for the maximal independent set problem, Proc. 17th ACM STOC (1985) 1–10.

    Google Scholar 

  11. E. Speckenmeyer, Untersuchungen zum Feedback Vertex Set Problem in ungerichteten Graphen, Ph.D. Thesis, Universität Paderborn, 1983.

    Google Scholar 

  12. T. Watanabe, T. Ae and A. Nakamura, On the removal of forbidden graphs by edge-deletion or by edge-contraction, Discrete Appl. Math. 3 (1981) 151–153.

    Google Scholar 

  13. M. Yannakakis, Node-deletion problems on bipartite graphs, SIAM J. Comput. 10 (1981) 310–327.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB 17, Mathematik-Informatik, Universität Paderborn, 4790, Paderborn, West Germany

    Satoru Miyano

  2. Department of Mathematics, Kyushu University 33, 812, Fukuoka, Japan

    Satoru Miyano

Authors
  1. Satoru Miyano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Thomas Ottmann

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Miyano, S. (1987). The lexicographically first maximal subgraph problems: P-completeness and NC algorithms. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_36

Download citation

  • DOI: https://doi.org/10.1007/3-540-18088-5_36

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18088-3

  • Online ISBN: 978-3-540-47747-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation