Bounds on the Size of the TBR Unit-Neighbourhood

摘要

In this paper, we study the unit-neighbourhood of the tree bisection and reconnection operation on unrooted binary phylogenetic trees. Specifically, we provide a recursive method to calculate the size of the unit-neighbourhood for any tree in the space fancyscriptT_n{fancyscript{T}_n} of unrooted binary phylogenetic trees with n-leaves. We also give both upper and lower bounds on this size for all trees in fancyscriptT_n{fancyscript{T}_n}, and characterize those trees for which the stated upper bound is sharp.