  We show that the graded maximal ideal of a graded $K$-algebra $R$ has linear
quotients for a suitable choice and order of its generators if the defining
ideal of $R$ has a quadratic Gr\"obner basis with respect to the reverse
lexicographic order, and show that this linear quotient property for algebras
defined by binomial edge ideals characterizes closed graphs. Furthermore, for
algebras defined by binomial edge ideals attached to a closed graph and for
join-meet rings attached to a finite distributive lattice we present explicit
Koszul filtrations.
