Prove or disprove. Let \(T\) be a minimal spanning tree of an undirected graph \(G\) and fix a vertex \(v_{0}\). Then for each vertex \(u eq v_{0}\), the cost of the path in \(T\) from \(v_{0}\) to \(u\) is minimal among all paths in \(G\) from \(v_{0}\) to \(u\).