On the existence of properly colored factors in edge colored graphs

In 1952, W.T.Tutte proved his celebrated “factor" theorem. We first
review necessary and sufficient conditions for the existence of factors
in graphs. Then we will show how to extend them to the colored version.
We also present related complexity results. Joint work with M. Furuya,
K. Kimura, K. Ozeki, Ch. Purcell and T. Yashima.