Skip to main content
SpringerLink
Log in

LexBFS-Ordering in Asteroidal Triple-Free Graphs

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1741))

Included in the following conference series:

Abstract

In this paper, we study the metric property of LexBFS- ordering on AT-free graphs. Based on a 2-sweep LexBFS algorithm, we show that every AT-free graph admits a vertex ordering, called the strong 2-cocomparability ordering, that for any three vertices u ≺ v ≺ w in the ordering, if d(u,w) ≤ 2 then d(u, v) = 1 or d(v,w) ≤ 2. As an application of this ordering, we provide a simple linear time recognition algorithm for bipartite permutation graphs, which form a subclass of AT-free graphs.

This work was supported by the National Science Council, Republic of China under grant NSC89-2213-E-008-007.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Brandstädt, V. B. Le and J. P. Spinrad, Graph Classes: A Survey, (series SIAM Monographs on Discrete Mathematics and Applications, 1999).

    Google Scholar 

  2. K. S. Booth and G. S. Lueker, Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms, J. Comput. System Sci., 13 (1976) 335–379.

    Google Scholar 

  3. H. Broersma, T. Kloks, D. Kratsch and H. Muller, Independent sets in asteroidal triple-free graphs, SIAM J. Discrete Math., 12 (1999) 276–287.

    Google Scholar 

  4. J. M. Chang, C. W. Ho and M. T. Ko, Distances in asteroidal triple-free graphs and their powers, in: Proceedings of CTS Workshop on Combinatorics and Algorithms, Taipei, Taiwan, (1998) 1–14.

    Google Scholar 

  5. D. G. Corneil, F. F. Dragan, M. Habib and C. Paul, Diameter determination on restricted graph families, in: Proceedings of WG’98, LNCS Vol. 1517, Springer-Verlag, (1998) 192–202.

    Google Scholar 

  6. D. G. Corneil, S. Olariu and L. Stewart, A linear time algorithm to compute a dominating path in an AT-free graph, Inform. Process. Lett., 54 (1995) 253–257.

    Google Scholar 

  7. D. G. Corneil, S. Olariu and L. Stewart, Asteroidal triple-free graphs, SIAM J. Discrete Math., 10 (1997), 399–430.

    Google Scholar 

  8. D. G. Corneil, S. Olariu and L. Stewart, Linear time algorithms for dominating pairs in asteroidal triple-free graphs, in: Proceedings of ICALP’95, LNCS Vol. 944, Springer-Verlag, (1995) 292–302.

    Google Scholar 

  9. T. Gallai, Transitiv orientierbare Graphen, Acta Math. Acad. Sci. Hung., 18 (1967) 25–66

    Google Scholar 

  10. M. C. Golumbic, C. L. Monma and W. T. Trotter, Jr. Tolerance graphs, Discrete Appl. Math., 9 (1984), 157–170.

    Google Scholar 

  11. C. T. Hoàng and B. A. Reed, P4-comparability graphs, Discrete Math., 74 (1989) 173–200.

    Google Scholar 

  12. B. Jamison and S. Olariu, On the semi-perfect elimination, Adv. Appl. Math., 9 (1988) 364–376.

    Google Scholar 

  13. T. Kloks, D. Kratsch and J. Spinrad, On treewidth and minimum fill-in of asteroidal triple-free graphs, Theor. Comput. Sci., 175 (1997) 309–335.

    Google Scholar 

  14. T. Kloks. H. Müller and C. K. Wong, Vertex ranking of asteroidal triple-free graphs, Inform. Process. Lett., 68 (1998) 201–206.

    Google Scholar 

  15. D. Kratsch, Domination and total domination on asteroidal triple-free graphs, Forschungsergebnisse Math/Inf/96/25, FSU Jena, Germany, 1996.

    Google Scholar 

  16. D. Kratsch, H. O. Le, H. Müller and E. Prisner, Additive tree spanners, manuscript, 1998.

    Google Scholar 

  17. C. G. Lekkerkerker and J. C. Boland, Representation of a finite graph by a set of intervals on the real line, Fund. Math., 51 (1962) 45–64.

    Google Scholar 

  18. A. Pnueli, A. Lempel and S. Even, Transitive orientation of graphs and identification of permutation graphs, Canad. J. Math., 23 (1971) 160–175.

    Google Scholar 

  19. D, J. Rose, Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32 (1970) 597–609.

    Google Scholar 

  20. D. J. Rose, R. E. Tarjan and G. S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5 (1976) 266–283.

    Google Scholar 

  21. J. Spinrad, Transitive orientation in O(n2) time, in: Proceedings of 15th Ann. ACM Symp. on Theory of Computing, (1983) 457–466.

    Google Scholar 

  22. J. Spinrad, A. Brandstädt and L. Stewart, Bipartite permutation graphs, Discrete Appl. Math., 18 (1987) 279–292.

    Google Scholar 

  23. R. E. Tarjan and M. Yanakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput., 13 (1984) 566–579.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science and Information Engineering, National Central University, Chung-Li, Taiwan, ROC

    Jou-Ming Chang & Chin-Wen Ho

  2. Institute of Information Science, Academia Sinica, Taipei, Taiwan, ROC

    Ming-Tat Ko

  3. Department of Information Management, National Taipei College of Business, Taipei, Taiwan, ROC

    Jou-Ming Chang

Authors
  1. Jou-Ming Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chin-Wen Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ming-Tat Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chang, JM., Ho, CW., Ko, MT. (1999). LexBFS-Ordering in Asteroidal Triple-Free Graphs. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-46632-0_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66916-6

  • Online ISBN: 978-3-540-46632-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation