Monotone bipartite graph properties are evasive

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