Skip to main content
Log in

On the recognition complexity of some graph properties

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

By applying a topological approach due to Kahn, Saks and Sturtevant, we prove that all decreasing graph properties consisting of bipartite graphs only are elusive. This is an analogue to a well-known result of Yao.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Aigner:Combinatorial Search, Wiley-Teubner, Stuttgart and Chichester, 1988.

    Google Scholar 

  2. M. R. Best, P. Van Emde Boas, H. W. Lenstra Jr.:A sharpened version of the Aanderaa-Rosenberg conjecture, Math. Centrum Tracts, Amsterdam, 1974.

    Google Scholar 

  3. B. Bollobás: Complete subgraphs are elusive,J. Combin. Theory B 21 (1976), 1–7.

    Article  Google Scholar 

  4. B. Bollobás:Extremal Graph Theory, Academic Press, London, 1978.

    Google Scholar 

  5. D. Grieser: Some results on the complexity of sets,Discrete Math. 88 (1991), 179–192.

    Article  Google Scholar 

  6. L. Kaloujnine: La structure desp-groupes de Sylow des groupes symétriques finis,Ann. Sci. Ecole Norm. Sup. (3),65, (1948), 239–276.

    Google Scholar 

  7. V. King: A lower bound for the recognition of digraph properties,Combinatorica 10 (1990), 53–59.

    Google Scholar 

  8. D.J. Kleitman and D.J. Kwiatkowski: Further results on the Aanderaa-Rosenberg conjecture,J. Combin. Theory B (1980), 85–95.

    Google Scholar 

  9. J. Kahn, M. Saks andD. Sturtevant: A topological approach to evasiveness,Combinatorica 4 (1984), 297–306.

    Google Scholar 

  10. A. Kerber: Algebraic Combinatorics via finite group actions, BI-Wissenschaftsverlag, Mannheim 1991.

    Google Scholar 

  11. R. Oliver: Fixed point sets of group actions on finite acyclic complexes,Comment. Math. Helv. 50 (1975), 155–177.

    Google Scholar 

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

    Article  Google Scholar 

  13. R. L. Rivest andJ. Vuillemin: On recognizing graph properties from adjacency matrices,Theor. Comput. Sci. 3 (1976/77), 371–384.

    Article  Google Scholar 

  14. P. A. Smith: Fixed point theorems for periodic transformations,Amer. J. Math. 63 (1941), 1–8.

    Google Scholar 

  15. E. H. Spanier:Algebraic topology, McGraw-Hill, New York, 1966.

    Google Scholar 

  16. E. Triesch:Elusive properties, in: Combinatorial Theory, Proceddings Schloß Rauischholzhausen (1982) (D. Jungnickel and K. Vedder, eds.), Springer Lecture Notes in Math., 321–326.

  17. E. Triesch:Über die Komplexität von Grapheneigenschaften, Dissertation, Aachen, 1984.

  18. E. Triesch: Some results on elusive graph properties,SIAM J. Comput. 23 (1994), 247–254.

    Article  Google Scholar 

  19. A. C-C. Yao: Monotone bipartite graph properties are evasive,SIAM J. Comput. 17 (1988), 517–520.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Triesch, E. On the recognition complexity of some graph properties. Combinatorica 16, 259–268 (1996). https://doi.org/10.1007/BF01844851

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01844851

Mathematics Subject Classification (1991)

Navigation