On the neighbourhoods of trees

Details On the neighbourhoods of trees On the neighbourhoods of trees

2012-02-10

arxiv.org/abs/1202.2203v1

Mathematics

Combinatorics

17 pages

Scientific paper

Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighbourhood, that is, the number of trees exactly one operation from a given tree. We present an expression for the size of the TBR (tree bisection and reconnection) neighbourhood, thus answering a question first posed in [Annals of Combinatorics, 5, 2001 1-15].

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