Edgy

You are given a tree with $N$ vertices (numbered $1$ through $N$). Each edge of this tree is coloured either black or white. A *single-colour subtree* of this tree is a non-empty maximal set $S$ of its edges such that all edges in $S$ have the same colour and each of these edges can be reached from any other edge in $S$ by only traversing edges from $S$. A maximal set is a set to which we cannot