Restricted Matchings and Edge Colorings

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Matchings in graphs are one of the most fundamental and well-studied objects in combinatorial optimization. Their investigation has led to some of the most classical concepts, results, and algorithms in this field, and several types of restricted matchings have been proposed. In this project we want to approach problems concerning induced matchings, uniquely restricted matchings, and degenerate matchings, as well as the corresponding edge colorings. We will focus on structural results, bounds, exact and approximative algorithms.