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#### Unicyclic Networks: Compatibility and Enumeration

(University of Canterbury. Mathematics and Statistics., 2006)

Graphs 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 ...

#### Bounding the Number of Hybridisation Events for a Consistent Evolutionary History

(University of Canterbury. Mathematics and Statistics., 2005)

#### Four characters suffice to convexly define a phylogenetic tree

(University of Canterbury. Mathematics and Statistics, 2005)

It was recently shown that just five characters (functions on a finite set X) suffice to convexly define a trivalent tree with leaf set X. Here we show that four characters suffice which, since three characters is not ...

#### Counting Ancestral Reconstructions in a Fixed Phylogeny

(University of Canterbury. Mathematics and Statistics, 2008)

We give formulas for calculating in polynomial time the number of ancestral reconstructions for a tree with binary leaf- and root labels for each number of 0 → 1 and 1 → 0 arcs. For trees of fixed degree, the corresponding ...

#### Tree reconstruction via a closure operation on partial splits

(Springer-VerlagUniversity of Canterbury. Mathematics and Statistics., 2001)

A fundamental problem in biological classi cation is the reconstruction of phylogenetic trees for a set X of species from a collection of either subtrees or qualitative characters. This task is equivalent to tree reconstruction ...