Using the Hecke insertion algorithm of Buch-Kresh-Shimozono-Tamvakis- Yong, we define a K-theoretic analogue of Fomin´s dual graded graphs called dual filtered graphs. The key formula in the definition is DU-UD=D+I. We discuss two main constructions of dual filtered graphs: the Mobius construction, which corresponds to natural insertion algorithms, and the Pieri construction, which is an algebraic construction. We end with some enumerative results using up- down calculus. This is work with Pasha Pylyavskyy.