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Some problems in permutation graphs

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Combinatorial Mathematics III

Part of the book series: Lecture Notes in Mathematics ((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.

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References

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

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  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.

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

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  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).

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

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

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

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

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Melbourne, Parkville, Victoria

    D. A. Holton & K. C. Stacey

Authors
  1. D. A. Holton
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  2. K. C. Stacey
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Editor information

Anne Penfold Street Walter Denis Wallis

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© 1975 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive

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