  There are many different classifications of entanglement for multipartite
quantum systems, one of which is based on the number of unentangled particles.
In this paper, we mainly study the quantum states containing at most $k-1$
unentangled particles and provide several entanglement criteria based on
different forms of inequalities which can both identify quantum states
containing at most $k-1$ unentangled particles. We show that these criteria are
more effective for some states by concrete examples.
