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Phylogenetic trees are a commonly used tool for representing the relationships between species in an evolutionary system, especially in evolutionary biology. A central task in the study of these trees is to determine which among a set of hypothesised trees gives the best explanation of empirical data. However, finding the trees that optimize some criterion… (More)

- Yang Ding, Stefan Grünewald, Peter J. Humphries
- J. Comb. Theory, Ser. A
- 2011

- Peter J. Humphries, Taoyang Wu
- IEEE/ACM Transactions on Computational Biology…
- 2013

Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighborhood, that is, the number of trees exactly one operation from a given tree. We present an exact expression for the size of the TBR (tree bisection and reconnection) neighborhood, thus answering a… (More)

- Stefan Grünewald, Peter J. Humphries, Charles Semple
- Electr. J. Comb.
- 2008

A collection P of phylogenetic trees is compatible if there exists a single phylogenetic tree that displays each of the trees in P. Despite its computational difficulty, determining the compatibility of P is a fundamental task in evolutionary biology. Characterizations in terms of chordal graphs have been previously given for this problem as well as for the… (More)

- James F. Geelen, Peter J. Humphries
- SIAM J. Discrete Math.
- 2006

Rota conjectured that, given n disjoint bases of a rank-n matroid M , there are n disjoint transversals of these bases that are all bases of M . We prove a stronger statement for the class of paving matroids.

- Peter J. Humphries, Charles Semple
- Appl. Math. Lett.
- 2009

For two rooted phylogenetic trees T and T ′, the rooted subtree prune and regraft distance between T and T ′ has often been used as a replacement for the hybridization number of T and T ′. However, Baroni et al. [1] constructed particular instances that showed both the difference and the ratio between this number and distance can be arbitrarily large. In… (More)

- Peter J Humphries, Simone Linz, Charles Semple
- Bulletin of mathematical biology
- 2013

Recently, we have shown that calculating the minimum-temporal-hybridization number for a set [Formula: see text] of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when [Formula: see text] consists of exactly two trees. In this paper, we give the first characterization of the problem for [Formula: see text] being… (More)

- Peter J. Humphries, Simone Linz, Charles Semple
- Discrete Applied Mathematics
- 2013

Phylogenetic networks are now frequently used to explain the evolutionary history of a set of species for which a collection of gene trees, reconstructed from genetic material of different parts of the species’ genomes, reveal inconsistencies. However, in the context of hybridization, the reconstructed networks are often not temporal. If a hybridization… (More)

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