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Parity Splits by Triple Point Distances in X-Trees
Jörgen Backelin1 and Svante Linusson2
1Department of Mathematics, Stockholms Universitet, SE-106 91 Stockholm, Sweden
2Department of Mathematics, KTH, SE-100 44, Stockholm, Sweden
Annals of Combinatorics 10 (1) p.1-18 March, 2006
AMS Subject Classification: 05C60; 05C05, 05C12, 92D99
At the conference Andreas Dress defined parity split maps by triple point distance and asked for a characterisation of such maps coming from binary phylogenetic X-trees. This article gives an answer to that question. The characterisation for X-trees can be easily described as follows: If all restrictions of a split map to sets of five or fewer elements is a parity split map for an X-tree, then so is the entire map. To ensure that the parity split map comes from an X-tree which is binary and phylogenetic, we add two more technical conditions also based on studying at most five points at a time.
Keywords: phylogenetic tree, semilabelled, X-tree, graph metric, parity split


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