摘要：Almost 40 years ago, Anderan and Rosenberg conjectured that all non-trivial montone graph properties on n vertices have decision tree complexity at least rn for some r>0. It was first proved by Rivest and Vuillemin with r=1/6 and improved by Kleitman and Kwiatkoawski to r=1/9. In 1984, Kahn, Sake and Sturtevant developed ar a topological approach to the problem and improved r to 1/4. Recently, we succeeded in improving the value of r to 1/3 (joint work with R. Scheidweiler). In the talk, we give a sketch of the the proof. Moreover, we discuss the history of the problem and the method developed.