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A Novel Insight into the Perfect Phylogeny Problem
S. Grünewald1 and K.T. Huber2
1AllanWilson Centre for Molecular Ecology and Evolution and Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
S.Grunewald@math.canterbury.ac.nz
2School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, United Kingdom
Katharina.Huber@cmp.uea.ac.uk
Annals of Combinatorics 10 (1) p.97-109 March, 2006
AMS Subject Classification: 05C05, 92D15
Abstract:

One of the classical problem in computational biology is the character compatibility problem or perfect phylogeny problem. A standard formulation of this problem in terms of two closely related questions is the following. Given a data set consisting of a finite set X and a set R of partitions induced on X by a set of characters. Is R compatible, that is, does there exist an evolutionary tree that represents (in a well-defined sense) the data? If this is the case, is this tree unique? A fundamental result in phylogenetics states that the answer to the former of the two questions is yes precisely if the partition intersection graph IR associated to R can be made chordal by obeying a certain rule.

The main insight from this paper is that the relation graph GR associated to a set R of partitions may provide a key for deciding whether such a chordalization of IR exists. To prove our results, we introduce an extension of the concept of the partition intersection graph associated to R using GR.
Keywords: perfect phylogeny problem, relation graph, compatibility, partition intersection graph, strictly represent, properly represent

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