Article

Combinatorica

, Volume 30, Issue 6, pp 735-743

First online:

An asymptotic bound for the complexity of monotone graph properties

  • Torsten KorneffelAffiliated with
  • , Eberhard TrieschAffiliated withLehrstuhl II für Mathematik, RWTH Aachen Email author 

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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 ¼n 2, 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)

05C25 05C99 68Q17