  In this paper, we consider a relation between $k$-way expansion constant of a
finite graph and the expansion constants of subgraphs in a $k$-partition of the
graph. Using this relation, we show that a sequence of finite graphs which have
uniformly bounded $k+1$-way expansion constants and uniformly bounded degrees
can be divided into $k$ or less sequences of expanders. Furthermore, we prove
that such sequence of finite graphs is not coarsely embeddable into any Hilbert
space.
