We prove that if the d-regular multigraph does not contain more than ⌊d/2⌋ copies of any 2-cycles then we can find a similar decomposition into n2 pairs of cycle covers where each 2-cycle occurs in at most one component of each pair.Expand

A dynamic forest of unrooted trees over a set of nvertices which we update by linkoperations: Each link operation adds a new edge adjacent to vertices in two different trees.Expand

In the classical union-find problem we maintain a partition of a universe of <i>n</i> elements into disjoint sets subject to the operations union and find.Expand

A novel variant of the problem of efficiently maintaining a forest of dynamic rooted trees, in which arbitrary arc deletions (cuts) do not occur, we give a method that takes O(log n) time per operation, including merging.Expand

Consider a dynamic forest of unrooted trees over a set of n vertices which we update by link operations: Each link operation adds a new edge adjacent to vertices in two different trees. Every edge in… Expand