We consider ${omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.