, Volume 11, Issue 2, pp 131–143 | Cite as

An Ω(n4/3) lower bound on the randomized complexity of graph properties

  • Péter Hajnal


We improve King's Ω(n5/4) lower bound on the randomized decision tree complexity of monotone graph properties to Ω(n4/3). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.

AMS subject classification code (1980)

68 Q 15 05 C 35 05 C 80 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Angluin, andL. G. Valiant: Fast probabilistic algorithms for Hamiltonian circuits and matchings,Journal of Computer and System Sciences,19, 155–193.Google Scholar
  2. [2]
    B. Bollobás:Extremal Graph theory, Chapter VIII., Academic Press, 1978.Google Scholar
  3. [3]
    P. A. Catlin: Subgraphs of graphs I.,Discrete Math. 10 (1974), 225–233.Google Scholar
  4. [4]
    H. Chernoff: A measure of asymptotic effiency for tests of a hypothesis based on the sum of observations,Annals of Math. Stat.,23 (1952), 493–509.Google Scholar
  5. [5]
    V. King: An Ω(n 5/4) lower bound on the randomized complexity of graph properties,Combinatorica,11 (1) (1991), 47–56.Google Scholar
  6. [6]
    J. Kahn, M. Saks, andD. Sturtevant: A topological aproach to evasiveness,Combinatorica,4(4) (1984), 297–306.Google Scholar
  7. [7]
    L. Lovász:Combinatorial Problems and Exercises, North-Holland 1979.Google Scholar
  8. [8]
    A. L. Rosenberg: On the time required to recognize properties of graphs: A problem,SIGACT News,5 (4) (1973), 15–16.Google Scholar
  9. [9]
    R. Rivest, andJ. Vuillemin: A generalization and proof of the Aanderaa-Rosenberg conjecture,Proc. 7th SIGACT Conference, (1975), ACM 1976.Google Scholar
  10. [10]
    N. Sauer, andJ. Spencer: Edge-disjoint replacement of graphs,J. of Combinatorial Theory Ser. B25 (1978), 295–302.Google Scholar
  11. [11]
    A. Yao: Probabilistic computation: towards a unified measure of complexity,Proc. 18th IEEE FOCS, 1977, pp. 222–227.Google Scholar
  12. [12]
    A. Yao: Lower bounds to randomized algorithms for graph properties,Proc. 28th IEEE FOCS, 1987, pp. 393–400.Google Scholar

Copyright information

© Akadéiai Kiadó 1991

Authors and Affiliations

  • Péter Hajnal
    • 1
    • 2
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA
  2. 2.Bolyai InstituteUniversity of SzegedHungary

Personalised recommendations