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Unicyclic networks: compatibility and enumeration

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2 Author(s)
Semple, C. ; Dept. of Math. & Stat., Canterbury Univ., Christchurch ; Steel, M.

Graphs obtained from a binary leaf labeled ("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 multicyclic networks

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Computational Biology and Bioinformatics, IEEE/ACM Transactions on  (Volume:3 ,  Issue: 1 )