The Schur functions are an important basis for the ring of symmetric functions. The Schur functions also have important applications in a number of topics in math including representation theory and Schubert calculus. However, it is often quite difficult to express a symmetric function in terms of Schur functions. For a number of functions, we must first express them in the larger ring of quasisymmetric functions. In 2007 Sami Assaf introduced dual equivalence graphs as a method for gathering quasisymmetric functions into a Schur function. The method involves the creation of a graph whose vertices are weighted quasisymmetric functions so that the sum of the weights of a connected component is a single Schur function. In this talk, we present a number of our results with regard to dual equivalence graphs. In particular we improve on Assaf's axiomatization of such graphs, giving locally testable criterion that are more easily verified by computers. As an application, we then apply these techniques to give explicit Schur expansions for a family of Lascoux-Leclerc-Thibon polynomials and Macdonald polynomials.