Degree constrained subgraphs

In this paper, we present new structural results about the existence of a subgraph where the degrees of the vertices are pre-specified. Further, we use these results to prove a 16-edge-weighting version of a conjecture by Karoński, Łuczak and Thomason, an asymptotic 2-edge-weighting version of the same conjecture, and a 78 version of Louigi's Conjecture.