Related papers: Displaying trees across two phylogenetic networks

Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…

We consider the polyhedral properties of two spanning tree problems with additional constraints. In the first problem, it is required to find a tree with a minimum sum of edge weights among all spanning trees with the number of leaves less…

We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is…

Phylogenomics heavily relies on well-curated sequence data sets that consist, for each gene, exclusively of 1:1-orthologous. Paralogs are treated as a dangerous nuisance that has to be detected and removed. We show here that this severe…

Structural parameters of graphs, such as treewidth, play a central role in the study of the parameterized complexity of graph problems. Motivated by the study of parametrized algorithms on phylogenetic networks, scanwidth was introduced…

In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely open. For instance, even the asymptotic counting problem for…

The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…

Galled trees are studied as a recombination model in theoretic population genetics. This class of phylogenetic networks has been generalized to tree-child networks, normal networks and tree-based networks by relaxing a structural condition.…

Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are…

We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…

For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…

Compatibility of phylogenetic trees is the most important concept underlying widely-used methods for assessing the agreement of different phylogenetic trees with overlapping taxa and combining them into common supertrees to reveal the tree…

Reconstructing a parsimonious phylogenetic network that displays multiple phylogenetic trees is an important problem in theory of phylogenetics, where the complexity of the inferred networks is measured by reticulation numbers. The…

We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.

A geophylogeny is a phylogenetic tree (or dendrogram) where each leaf (e.g. biological taxon) has an associated geographic location (site). To clearly visualize a geophylogeny, the tree is typically represented as a crossing-free drawing…

Phylogenetic trees are pervasively used to depict evolutionary relationships. Increasingly, researchers need to visualize large trees and compare multiple large trees inferred for the same set of taxa (reflecting uncertainty in the tree…

We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks…

Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network…

In phylogenetics, it is important for the phylogenetic network model parameters to be identifiable so that the evolutionary histories of a group of species can be consistently inferred. However, as the complexity of the phylogenetic network…

A multilabeled tree (or MUL-tree) is a rooted tree in which every leaf is labelled by an element from some set, but in which more than one leaf may be labelled by the same element of that set. In phylogenetics, such trees are used in…