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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References
Allen B.L., Steel M.: Subtree transfer operations and their induced metrics on evolutionary trees. Ann. Combin. 5(1), 1–15 (2001)
Hein J.: A heuristic method to reconstruct the history of sequences subject to recombination. J. Mol. Evol. 36(4), 369–405 (1993)
Maddison D.R.: The discovery and importance of multiple islands of most-parsimonious trees. Syst. Zool. 40(3), 315–328 (1991)
Robinson D.F.: Comparison of labeled trees with valency three. J. Combin. Theory Ser. B 11(2), 105–119 (1971)
Song Y.S.: On the combinatorics of rooted binary phylogenetic trees. Ann. Combin. 7(3), 365–379 (2003)
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Humphries, P.J. Bounds on the Size of the TBR Unit-Neighbourhood. Ann. Comb. 14, 479–485 (2010). https://doi.org/10.1007/s00026-011-0072-y
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DOI: https://doi.org/10.1007/s00026-011-0072-y