Maintenance of a minimum spanning forest in a dynamic planar graph
David Eppstein, Giuseppe F. Italiano, Roberto Tamassia, Robert E. Tarjan, Jeffery R. Westbrook, and Moti Yung
J. Algorithms 15:173, 1993
Mathematical Reviews 94b:68039, 1994
The merge operation defined on page 44 is incompletely defined. The merge operation requires that the vertices $u$ and $v$ to be merged belong to different trees. Otherwise the merging can produce a cycle.