In this paper we extend the concept of weakly polymatroidal ideals to monomial ideals which are not necessarily generated in one degree, and show that any ideal in this class has linear quotients. As an application we study some vertex cover ideals of weighted hypergraphs.
"Weakly polymatroidal ideals with applications to vertex cover ideals." Osaka J. Math. 47 (3) 627 - 636, September 2010.