Abstract
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 \({\fancyscript{T}_n}\) of unrooted binary phylogenetic trees with n-leaves. We also give both upper and lower bounds on this size for all trees in \({\fancyscript{T}_n}\), and characterize those trees for which the stated upper bound is sharp.
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