I am dealing with the following statement:
the run time for Dijkstra's on a connected undirected graph with positive edge weights using a binary heap is $\Theta$ of the run time for Kruskal's using union-find.
However, this is false and I fail to see why this is so. Dijkstra's algorithm when using binary heap is $O(|E|\log|V|)$. The same is true for Kruskal's algorithm as its complexity is $O(|E|\log|V|)$.
Hence, can someone reconcile this difference? Are there certain edge cases for when this isn't true, hence making this statement false?