Restricted Matchings and Edge Colorings

图中的匹配是组合优化中最基本和最受研究的对象之一。他们的研究导致了该领域中一些最经典的概念、结果和算法，并提出了几种类型的限制匹配。在这个项目中，我们想要探讨关于诱导匹配、唯一限制匹配、退化匹配以及相应的边染色的问题。我们将专注于结构结果、界、精确和近似算法。

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.