Filtered K-theory for graph algebras

We introduce filtered algebraic \(K\)-theory of a ring \(R\) relative to a sublattice of ideals. This is done in such a way that filtered algebraic \(K\)-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge invariant filtered \(K\)-theory for graph \(C^*\)-algebras. We apply this to verify the Abrams-Tomforde conjecture for a large class of finite graphs.