Consider the following variant of the Minimum Spanning Tree $($MST$)$ problem. We are given an undirected graph G $=($V$,$E$)$ with n vertices $($numbered from $0$ to n $1)$ and m edges, a positive $($not necessarily unique$)$ edge cost ce for each edge in E$,$ and a subset of edges A $$ E $($note that A may contain cycles$).$ Suppose that E represents a set of possible direct fibre links between vertices and A represents the existing set of direct fibre links between vertices. We would like to find the ch