On the distribution of lengths of evolutionary trees
SIAM Journal on Discrete Mathematics
Reconstructing reticulate evolution in species: theory and practice
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Combinatorial Enumeration
Phylogenetic Networks: Modeling, Reconstructibility, and Accuracy
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Phylogenetic Super-Networks from Partial Trees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The maximum agreement of two nested phylogenetic networks
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Reconstruction of reticulate networks from gene trees
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Constructing a smallest refining galled phylogenetic network
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Intersection representations of matrices by subtrees and unicycles on graphs
Journal of Discrete Algorithms
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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{\hbox{-}}{\rm 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.