Given $G=(V,E)$ undirected, connected graph and weights given by $w:E \to \mathbb R$. We also know that $|E|=|V|+87$.
Find Minimum spanning tree of $G$.
Obviously we can use Prim in $O(|V| \cdot \log |V|)$.
But can we do better by using the fact that the graph is connected, and use the sets sizes? Like removing the lightest edge from each cycle and keeping the connectivity of the graph?