Combinatorica

, Volume 30, Issue 6, pp 735–743

An asymptotic bound for the complexity of monotone graph properties

Authors

  • Torsten Korneffel
    • Lehrstuhl II für MathematikRWTH Aachen
Article

DOI: 10.1007/s00493-010-2485-3

Cite this article as:
Korneffel, T. & Triesch, E. Combinatorica (2010) 30: 735. doi:10.1007/s00493-010-2485-3

Abstract

We present an application of the topological approach of Kahn, Saks and Sturtevant to the evasiveness conjecture for monotone graph properties. Although they proved evasiveness for every prime power of vertices, the best asymtotic lower bound for the (decision tree) complexity c(n) known so far is ¼n2, proved in the same paper. In case that the evasiveness conjecture holds, it is ½n(n−1).We demonstrate some techniques to improve the 1/4 bound and show \( c(n) \geqslant \tfrac{8} {{25}}n^2 - o(n^2 ) \).

Mathematics Subject Classification (2000)

05C2505C9968Q17

Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2010