This article provides structural characterization of simple graphs whose edge-set can be partitioned into maximum matchings. We use Vizing's classification of simple graphs based on edge chromatic index.
@article{arxiv.1210.4710,
title = {Graphs whose edge set can be partitioned into maximum matchings},
author = {Niraj Khare},
journal= {arXiv preprint arXiv:1210.4710},
year = {2012}
}