I tried to study the maximum matching for a line-graph , i.e , $L(G)$ of a graph , $G(V,E)$ , from here : https://www.sciencedirect.com/science/article/pii/S0012365X97001039
But could not understand it , can anybody explain it in detail .
I understood how to create the corresponding tree , but after that I could not understand the process of finding the maximum matching .