Resolvable cycle decompositions of complete multigraphs and complete equipartite multigraphs via layering and detachment

We construct new resolvable decompositions of complete multigraphs and equipartite into cycles variable lengths (and a perfect matching if the vertex degrees are odd). develop two techniques: layering, which allows us to obtain 2-factorizations from existing graphs, detachment, cycle multigraphs. These techniques applied specified type for both multigraphs, with emphasis on solutions Oberwolfach Problem Hamilton–Waterloo Problem. In addition, we show existence some thickly decompositions.