Hamiltonian Walks of Phylogenetic Treespaces
We answer Bryant's combinatorial challenge on minimal walks of phylogenetic treespace under the nearest-neighbor interchange (NNI) metric. We show that the shortest path through the NNI-treespace of n-leaf trees is Hamiltonian for all n. That is, there is a minimal path that visits all binary trees exactly once, under NNI moves.
phylogenetic tree construction graph theory analysis of algorithms