Skip to main content
SpringerLink
Log in

On greedy matching ordering and greedy matchable graphs

Extended Abstract

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1335))

Included in the following conference series:

Abstract

In this note a greedy algorithm is considered that computes a matching for a graph with a given ordering of its vertices, and those graphs are studied for which a vertex ordering exists such that the greedy algorithm always yields maximum cardinality matchings for each induced subgraph. We show that these graphs, called greedy matchable graphs, are a subclass of weakly triangulated graphs and contain strongly chordal graphs and chordal bipartite graphs as proper subclasses. The question when can this ordering be produced efficiently is discussed too.

Research supported by the VW, Project No. 1/69041, and by the DFG.

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. R.P. Anstee and M. Farber, Characterizations of totally balanced matrices, J. Algorithms, 5 (1984), 215–230.

    Google Scholar 

  2. G. Ausiello, D. D'ATRI and M. Moscarini, Chordality properties on graphs and minimal conceptual connections in semantic data models, J. Computer and System Sciences, 33 (1986), 179–202.

    Google Scholar 

  3. A. Brandstädt, Special graph classes-A survey, Schriftenreihe des Fachbereichs Mathematik, SM-DU-199, Universität Duisburg, 1991.

    Google Scholar 

  4. A. Brandstädt, F.F. Dragan and F. Nicolai, LexBFS-orderings and powers of chordal graphs, Discrete Math., 171 (1997), 27–42.

    Google Scholar 

  5. G. J. Chang AND G.L. Nemhauser, The k-domination and k-stability problems on sun-free chordal graphs, SIAM J. Alg. Discrete Meth., 5 (1984), 332–345.

    Google Scholar 

  6. E. Dalhaus and M. Karpinski, On the computational complexity of matching and multidimensional matching in chordal and strongly chordal graphs, Manuscript.

    Google Scholar 

  7. F.F. Dragan, F. Nicolai and A. Brandstädt, Convexity and HHD-free graphs, Technical Report Gerhard-Mercator-Universität-Gesamthochschule Duisburg SM-DU-290, 1995.

    Google Scholar 

  8. M. Farber, Characterization of strongly chordal graphs, Discrete Math., 43 (1983), 173–189.

    Google Scholar 

  9. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York 1980.

    Google Scholar 

  10. M.C. Golumbic and C.F. Goss, Perfect elimination and chordal bipartite graphs, J. Graph Theory, 2 (1978), 155–163.

    Google Scholar 

  11. R. Hayward, Weakly triangulated graphs, Journal of Combin. Theory (B), 39 (1985),200–209.

    Google Scholar 

  12. A.J. Hoffman, A.W.J. Kolen and M. Sakarovitch, Totally-balanced and greedy matrices, SIAM J. Alg. Disc. Meth., 6 (1985), 721–730.

    Google Scholar 

  13. E. Howorka, A characterization of distance-hereditary graphs, Quart. J. Math. Oxford Ser. 2, 28 (1977), 417–420.

    Google Scholar 

  14. E. Howorka, A characterization of ptolemaic graphs, J. Graph Theory, 5 (1981), 323–331.

    Google Scholar 

  15. B. Jamison and S. Olariu, On the serni-perfect elimination, Advances in Applied Math. 9 (1988), 364–376.

    Google Scholar 

  16. T. Kloks and D. Kratsch, Computing a perfect edge without vertex elimination ordering of a chordal bipartite graph, Information Processing Letters 55 (1995) 11–16.

    Google Scholar 

  17. L. Lovász and M.D. Plummer, Matching Theory, Ann. Discrete Math. 29 (1986).

    Google Scholar 

  18. A. Lubiw, Doubly lexical orderings of matrices, SIAM J. Comput. 16 (1987), 854–879.

    Google Scholar 

  19. R. Paige and R.E. Tarjan, Three partition refinement algorithms, SIAM J. Cornput., 16 (1987), 973–989.

    Google Scholar 

  20. W.R. Pulleyblank, Matching and Extensions, in Handbook of Combinatorics (L.R. Graham, et al., eds.), Elsevier (Amsterdam) 1995, vol. 1, pp. 179–232.

    Google Scholar 

  21. M. Queyranne, F. Spieksma and F. T'ardella, A general class of greedily solvable linear programs, 3rdIPCO Conference (G. Rinaldi and L. Wolsey, eds.), (1993) 385–399.

    Google Scholar 

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

    Google Scholar 

  23. J.P. Spinrad, Doubly lexical ordering of dense 0–1-matrices, Information Processing Letters 45 (1993) 229–235.

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Informatik, Lehrstuhl für Theoretische Informatik, Universität Rostock, D-18051, Rostock, Germany

    Feodor F. Dragan

Authors
  1. Feodor F. Dragan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rolf H. Möhring

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dragan, F.F. (1997). On greedy matching ordering and greedy matchable graphs. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024498

Download citation

  • DOI: https://doi.org/10.1007/BFb0024498

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63757-8

  • Online ISBN: 978-3-540-69643-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation