Title: $k$-shellable simplicial complexes and graphs,
Abstract: In this paper we show that a $k$-shellable simplicial complex is the
expansion of a shellable complex. We prove that the face ring of a pure
$k$-shellable simplicial complex satisfies the Stanley conjecture. In this way,
by applying expansion functor to the face ring of a given pure shellable
complex, we construct a large class of rings satisfying the Stanley conjecture.
Also, by presenting some characterizations of $k$-shellable graphs, we extend
some results due to Castrillón-Cruz, Cruz-Estrada and Van Tuyl-Villareal.