Generalizing the four gamete condition and splits equivalence theorem: perfect phylogeny on three state characters

Authors:
Fumei Lam;Dan Gusfield;Srinath Sridhar
Affiliations:
Department of Computer Science, University of California, Davis;Department of Computer Science, University of California, Davis;Department of Computer Science, Carnegie Mellon University
Venue:
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Year:
2009

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Abstract

We study the three state perfect phylogeny problem and show that there is a three state perfect phylogeny for a set of input sequences if and only if there is a perfect phylogeny for every subset of three characters. In establishing these results, we prove fundamental structural features of the perfect phylogeny problem on three state characters and completely characterize the obstruction sets that must occur in input sequences that do not have a perfect phylogeny. We also give a proof for a stated lower bound involved in the conjectured generalization of our main result to any number of states.