DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE ODENSE UNIVERSITY On Optimal Ear-Decompositions of Graphs Zoltan Szigeti Universite Paris VI Tuesday, November 5, 1996, at 2:15 PM The Seminar Room We give a short survey on the results concerning ear-decompositions. Particularly, we shall concentrate on optimal ear-decompositions containing minimum number of even ears. In the second part of the talk we shall investigate matching-covered graphs. A connected graph G is matching-covered if each edge belongs to some perfect matching of G. A short and simple proof will be given for the ``Two Ear Theorem'' of Lovasz and Plummer on matching-covered graphs. Joergen Bang-Jensen