Monotone Bipartite Graph Properties are Evasive

Abstract:

A Boolean function P from {0,1}t into {0,1} is said to be evasive, if every decision tree algorithm for evaluating P must examine at least t arguments in the worst case. It was known that any nontrivial monotone bipartite graph property on vertex set V x W must be evasive, when |V| x |W| is a power of
a prime number. In this paper, we prove that every nontrivial monotone bipartite graph property is evasive.