f-Vectors Implying Vertex Decomposability

摘要

We prove that if a pure simplicial complex (Delta ) of dimension (d) with (n) facets has the least possible number of ((d-1))-dimensional faces among all complexes with (n) faces of dimension (d), then it is vertex decomposable. This answers a question of J. Herzog and T. Hibi. In fact, we prove a generalization of their theorem using combinatorial methods.