Postorder Disjoint Set Union is Linear
Joan M. Lucas · SIAM Journal on Computing · 1990
Any instance of the disjoint set union problem of size n, using any union strategy, that does one find per node in postorder has total cost $O(n)$. This special case, when the finds are restricted to occur in postorder, is related to the behavior of such self-adjusting data structures as the splay tree and the pairing heap.