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Computational complexity of graph properties

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1073)

Abstract

We prove some general properties are elusive, generalize some results on the Aanderaa-Rosenberg conjecture, find some necessary conditions for certain properties to be non-elusive and produce some non-elusive properties.

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References

  1. B. Alspach, Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree, J. Comb. Theory, Ser. B, 15 (1973), 12–17.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. M. R. Best, P. van Emde Boas and H. W. Lenstra Jr., A Sharpened version of the Aanderaa-Rosenberg conjecture, Math. Centrum, Amsterdam, 1974.

    Google Scholar 

  3. B. Bollobàs, Complete subgraphs are elusive, J. Comb. Theory, Ser. B, 21 (1976), 1–7.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. B. Bollobàs, Extremal Graph Theory, Academic Press, London 1978.

    MATH  Google Scholar 

  5. B. Bollobàs and S. E. Eldridge, Packings of graphs and applications to computational complexity, J. Comb. Theory, Ser. B, 25 (1978), 105–124.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. R. C. Holt and E. M. Reingold, On the time required to detect cycles and connectivity in graphs, Math. Syst. Theory, 6 (1972), 103–106.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. J. Hopcroft and R. Tarjan, Efficient planarity testing, TR73-165, Department of Computer Science, Cornell University, April, 1973.

    Google Scholar 

  8. D. Kirkpatrick, Determining graph properties from matrix representations, in "Proc. 6th SIGACT Conference, Seattle, 1974", pp.84–90.

    Google Scholar 

  9. Norbert Illies, A counter-example to the Generalized Aanderaa-Rosenberg Conjecture, Information Process. Lett. Vol. 7, No. 3, (1978), 154–155.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. D. Kleitman and D. J. Kwiatkowski, Further results on the Aanderaa-Rosenberg conjecture, J. Comb. Theory, Ser. B, 28 (1980), 85–95.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. R. J. Lipton and L. Snyder, On the Aadneraa-Rosenberg conjecture, SIGACT News 6 (Jan., 1974), 30–31.

    CrossRef  Google Scholar 

  12. E. C. Milner and D. J. A. Welsh, On the computational complexity of graph theoretical properties, University of Calgary, Research Paper No.232, June, 1974.

    Google Scholar 

  13. E. C. Milner and D. J. A. Welsh, On the computational complexity of graph theoretical properties, in "Proc. Fifth British Combinatorial Conf." (C. St. J. A. Nash-Williams and J. Sheehan, eds.), Congressus Numerantium XV, 1975, pp.471–487.

    Google Scholar 

  14. R. L. Rivest and J. Vuillemin, On the time required to recognize properties of graphs from their adjacency matrices (Revised), UC Berkeley Electronics Research Laboratory, Memorandum No.ERL-M476, November, 1974.

    Google Scholar 

  15. R. L. Rivest and J. Vuillemin, A generalization and proof of the Aanderaa-Rosenberg conjecture, Proceedings of Seventh Annual ACM Symposium on Theory of Computing (1975), 6–11.

    Google Scholar 

  16. R. L. Rivest and J. Vuillemin, On recognizing graph properties from adjacency matrices, Theor. Comput. Sci. 3 (1976), 371–384.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. A. L. Rosenberg, On the time required to recognize properties of graphs: a problem, SIGACT News 5 (Oct., 1973), 15–16.

    CrossRef  Google Scholar 

  18. R. Tarjan, Depth-first search and linear graph algorithms, SIAM J. Comput., Vol.1, No.2 (June, 1972), 146–159.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. J. Turner, Point-symmetric graphs with a prime number of points, J. Comb. Theory 3 (1967), 136–145.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1984 Springer-Verlag

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Yap, H.P. (1984). Computational complexity of graph properties. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073104

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  • DOI: https://doi.org/10.1007/BFb0073104

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13368-1

  • Online ISBN: 978-3-540-38924-8

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