12 papers · 1 filter
Arboreal Networks and Ultrametrics
Katharina T. Huber, Vincent Moulton, Guillaume E. Scholz
Ultametrics are an important class of distances used in applications such as phylogenetics, clustering and classification theory. Ultrametrics are essentially distances that can be…
Inferring DAGs and Phylogenetic Networks from Least Common Ancestors
Anna Lindeberg, Anton Alfonsson, Vincent Moulton +2
A least common ancestor (LCA) of two leaves in a directed acyclic graph (DAG) is a vertex that is an ancestor of both leaves and has no proper descendant that is also their common…
Representing distance-hereditary graphs with multi-rooted trees
Guillaume E. Scholz
Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is…
Network Representation and Modular Decomposition of Combinatorial Structures: A Galled-Tree Perspective
Anna Lindeberg, Guillaume E. Scholz, Marc Hellmuth
In phylogenetics, reconstructing rooted trees from distances between taxa is a common task. Böcker and Dress generalized this concept by introducing symbolic dated maps $δ:X \times…
The Complement of the Djokovic-Winkler Relation
Marc Hellmuth, Bruno J. Schmidt, Guillaume E. Scholz +1
The Djoković-Winkler relation is a binary relation defined on the edge set of a given graph that is based on the distances of certain vertices and which plays a prominent role…
Shared ancestry graphs and symbolic arboreal maps
Katharina T. Huber, Vincent Moulton, Guillaume E. Scholz
A network on a finite set , , is a connected directed acyclic graph with leaf set in which every root in has outdegree at least 2 and no vertex in has…