Unicyclic Networks: Compatibility and Enumeration

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dc.contributor.authorSemple, C.
dc.contributor.authorSteel, M.
dc.date.accessioned2008-10-23T22:27:57Z
dc.date.available2008-10-23T22:27:57Z
dc.date.issued2006en
dc.description.abstractGraphs obtained from a binary leaf labelled (‘phylogenetic’) tree by adding an edge so as to introduce a cycle provide a useful representation of hybrid evolution in molecular evolutionary biology. This class of graphs (which we call ‘unicyclic networks’) also has some attractive combinatorial properties, which we present. We characterize when a set of binary phylogenetic trees is displayed by a unicyclic network in terms of tree rearrangement operations. This leads to a triple-wise compatibility theorem, and a simple, fast algorithm to determine 1-cycle compatibility. We also use generating function techniques to provide closed-form expressions that enumerate unicyclic networks with specified or unspecified cycle length, and we provide an extension to enumerate a class of multi-cyclic networks.en
dc.identifier.citationSemple, C., Steel, M. (2006) Unicyclic Networks: Compatibility and Enumeration. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 3(1), pp. 84-91.en
dc.identifier.doihttps://doi.org/10.1109/TCBB.2006.14
dc.identifier.issn1545-5963
dc.identifier.urihttp://hdl.handle.net/10092/1720
dc.language.isoen
dc.publisherUniversity of Canterbury. Mathematics and Statistics.en
dc.rights.urihttps://hdl.handle.net/10092/17651en
dc.subjectphylogenetic treeen
dc.subjectcompatibilityen
dc.subjectcircular orderingsen
dc.subjectgenerating functionen
dc.subjectgalled-treesen
dc.subject.marsdenFields of Research::230000 Mathematical Sciences::239900 Other Mathematical Sciences::239901 Biological Mathematicsen
dc.titleUnicyclic Networks: Compatibility and Enumerationen
dc.typeJournal Article
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