## Search

Now showing items 21-30 of 161

#### Counting consistent phylogenetic trees is #P-complete

(University of Canterbury. Mathematics and Statistics., 2004)

Reconstructing phylogenetic trees is a fundamental task in evolutionary biology. Various algorithms exist for this purpose, many of
which come under the heading of `supertree methods'. These methods
amalgamate a collection ...

#### Replacing cliques by stars in quasi-median graphs

(University of Canterbury. Mathematics and Statistics., 2004)

For a multi-set Σ of splits (bipartitions) of a finite set X, we
introduce the multi-split graph G(Σ). This graph is a natural extension of
the Buneman graph. Indeed, it is shown that several results pertaining to
the ...

#### Identifying phylogenetic trees

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

A central problem that arises in evolutionary biology is that of
displaying partitions of subsets of a finite set X on a tree whose vertices are
partially labelled with the elements of X. Such a tree is called an ...

#### A chain theorem for matroids

(University of Canterbury. Mathematics and Statistics., 2008)

Tutte’s Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a
3-connected minor N such that |E(M)| - |E(N)| = 1. Geelen and Whittle extended this theorem by showing ...

#### The structure of the 3-separations of 3-connected matroids

(University of Canterbury. Mathematics and Statistics., 2004)

Tutte defined a k-separation of a matroid M to be a
partition (A,B) of the ground set of M such that ∣A∣,∣B∣ ≥ k and
r(A) + r(B) − r(M) < k. If, for all m < n, the matroid M has no
m-separations, then M is n-connected. ...

#### Optimizing phylogenetic diversity under constraints

(University of Canterbury. Mathematics and Statistics., 2007)

Phylogenetic diversity (PD) is a measure of the extent to which different subsets of taxa span an evolutionary tree, and provides a quantitative tool for studying biodiversity conservation. Recently, it was shown that the ...

#### Combinatorial Generation by Fusing Loopless Algorithms

(University of Canterbury. Computer Science and Software Engineering., 2007)

Some combinatorial generation problems can be broken down into subproblems
for which loopless algorithms already exist. We discuss means by which existing loopless
algorithms for subproblems can be combined or fused to ...

#### Encoding phylogenetic trees in terms of weighted quartets

(University of Canterbury. Mathematics and Statistics., 2008)

One of the main problems in phylogenetics is to develop systematic
methods for constructing evolutionary or phylogenetic trees. For a set
of species X, an edge-weighted phylogenetic X-tree or phylogenetic tree is
a ...

#### Negative correlation in graphs and matroids

(University of Canterbury. Mathematics and Statistics., 2008)

The following two conjectures arose in the work of Grimmett and Winkler, and Pemantle: the uniformly random forest F and the uniformly random connected subgraph C of a finite graph G have
the edge-negative-association ...

#### The structure of equivalent 3-separations in a 3-connected matroid

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

Let M be a matroid. When M is 2-connected, Cunningham and
Edmonds gave a tree decomposition of M that displays all of its 2-separations.
This result was extended by Oxley, Semple, and Whittle, who showed that,
when M ...