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Bounds on the Size of the TBR Unit-Neighbourhood
Peter J. Humphries
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
pjhumphries@gmail.com
Annals of Combinatorics 14 (4) pp.479-485 December, 2010
AMS Subject Classification: 05C05; 92D15
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 Jn of unrooted binary phylogenetic trees with n-leaves. We also give both upper and lower bounds on this size for all trees in Jn, and
characterize those trees for which the stated upper bound is sharp.
Keywords: tree bisection and reconnection, unit-neighbourhood, unrooted trees

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