Combinatorica

, Volume 16, Issue 2, pp 259–268 | Cite as

On the recognition complexity of some graph properties

  • Eberhard Triesch
Article

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.

Mathematics Subject Classification (1991)

68 Q 05 68 R 05 05 C 25 

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References

  1. [1]
    M. Aigner:Combinatorial Search, Wiley-Teubner, Stuttgart and Chichester, 1988.Google Scholar
  2. [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. [3]
    B. Bollobás: Complete subgraphs are elusive,J. Combin. Theory B 21 (1976), 1–7.CrossRefGoogle Scholar
  4. [4]
    B. Bollobás:Extremal Graph Theory, Academic Press, London, 1978.Google Scholar
  5. [5]
    D. Grieser: Some results on the complexity of sets,Discrete Math. 88 (1991), 179–192.CrossRefGoogle Scholar
  6. [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. [7]
    V. King: A lower bound for the recognition of digraph properties,Combinatorica 10 (1990), 53–59.Google Scholar
  8. [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. [9]
    J. Kahn, M. Saks andD. Sturtevant: A topological approach to evasiveness,Combinatorica 4 (1984), 297–306.Google Scholar
  10. [10]
    A. Kerber: Algebraic Combinatorics via finite group actions, BI-Wissenschaftsverlag, Mannheim 1991.Google Scholar
  11. [11]
    R. Oliver: Fixed point sets of group actions on finite acyclic complexes,Comment. Math. Helv. 50 (1975), 155–177.Google Scholar
  12. [12]
    A. L. Rosenberg:On the time required to recognize properties of graphs: a problem, SIGACT News 5 (1973), 15–16.CrossRefGoogle Scholar
  13. [13]
    R. L. Rivest andJ. Vuillemin: On recognizing graph properties from adjacency matrices,Theor. Comput. Sci. 3 (1976/77), 371–384.CrossRefGoogle Scholar
  14. [14]
    P. A. Smith: Fixed point theorems for periodic transformations,Amer. J. Math. 63 (1941), 1–8.Google Scholar
  15. [15]
    E. H. Spanier:Algebraic topology, McGraw-Hill, New York, 1966.Google Scholar
  16. [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.Google Scholar
  17. [17]
    E. Triesch:Über die Komplexität von Grapheneigenschaften, Dissertation, Aachen, 1984.Google Scholar
  18. [18]
    E. Triesch: Some results on elusive graph properties,SIAM J. Comput. 23 (1994), 247–254.CrossRefGoogle Scholar
  19. [19]
    A. C-C. Yao: Monotone bipartite graph properties are evasive,SIAM J. Comput. 17 (1988), 517–520.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Eberhard Triesch
    • 1
  1. 1.Forschungsinstitut für Diskrete MathematikBonnGermany

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