Doubt on underline 1 What do you mean by the edge subgraph of $G$ defined by $L$?IsIt a subgraph with all edges from $L$?
Doubt on underline 2 Why is the equality $|L \backslash M_H|=|L|-|M_H|$true? Why $|L\backslash M_H|\ge|U|$? Can you please explain?