Abstract :
We define the notion of a local adaptation of a spanning tree in a biconnected graph, and consider the number of local adaptations required to reconfigure the spanning tree. We show that ⌈n2⌉ ⌈n2 − 1⌉/2 local adaptations are sufficient, and may be necessary, to make a node a leaf in the spanning tree, that n28 + o(n2) local adaptations are sufficient, and may be necessary, to add or delete an edge from the spanning tree, and that 3n24 + o(n2) local adaptations are sufficient to transform one spanning tree to another spanning tree.
