Skip to main content

Some problems in permutation graphs

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 452)

Abstract

Some problems concerning the stability index of the permutation graph (Pn, π) are investigated. It is shown that for a certain class of permutation graphs, called Roman numerals, the stability index can be only 2n, 2n − 4, 2n − 5, 2n − 6 or 2n − 7. The general situation for (Pn, π) is more complicated and some open questions are listed.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Behzad and G. Chartrand, Introduction to the Theory of Graphs, (Allyn and Bacon, Boston, 1971).

    MATH  Google Scholar 

  2. Douglas D. Grant, The stability index of graphs, Combinatorial Mathematics: Proc. Second Austral. Conference, Lecture Notes in Maths., Vol. 403, Springer-Verlag, Berlin, Heidelberg, New York, (1974) to appear.

    Google Scholar 

  3. Douglas D. Grant, Stability and operations on graphs, this volume, 116–135.

    Google Scholar 

  4. S. Hedetniemi, On classes of graphs defined by special cutsets of lines, in The Many Facets of Graph Theory, Lecture Notes in Maths., Vol. 110, 171–190, Springer-Verlag, Berlin, Heidelberg, New York (1969).

    CrossRef  Google Scholar 

  5. D. A. Holton, Two applications of semi-stable graphs, Discrete Math., 4 (1973) 151–158.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D. A. Holton, A report on stable graphs, J. Austral. Math. Soc. 15, (1973), 163–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. D. A. Holton, Stable trees, J. Austral. Math. Soc. 15 (1973), 476–481.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. K. McAvaney, Douglas D. Grant and D. A. Holton, Stable and semistable unicyclic graphs, Discrete Math., to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Holton, D.A., Stacey, K.C. (1975). Some problems in permutation graphs. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069553

Download citation

  • DOI: https://doi.org/10.1007/BFb0069553

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive