112 citations · 255 across the 57 of their papers we have counts for
5 papers · 1 filter
Associativity and non-associativity of some hypergraph products
Richard H. Hammack, Marc Hellmuth, Lydia Ostermeier +1
Several variants of hypergraph products have been introduced as generalizations of the strong and direct products of graphs. Here we show that only some of them are associative. In…
Techniques for the Cograph Editing Problem: Module Merge is equivalent to Editing P4s
Marc Hellmuth, Adrian Fritz, Nicolas Wieseke +1
Cographs are graphs in which no four vertices induce a simple connected path . Cograph editing is to find for a given graph a set of at most edge additions and…
On Tree Representations of Relations and Graphs: Symbolic Ultrametrics and Cograph Edge Decompositions
Marc Hellmuth, Nicolas Wieseke
Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g.\ in phylogenomics. In this context symbo…
Fast Factorization of Cartesian products of Hypergraphs
Marc Hellmuth, Florian Lehner
Cartesian products of graphs and hypergraphs have been studied since the 1960s. For (un)directed hypergraphs, unique \emph{prime factor decomposition (PFD)} results with respect to…
On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions
Marc Hellmuth, Nicolas Wieseke
Symbolic ultrametrics define edge-colored complete graphs K_n and yield a simple tree representation of K_n. We discuss, under which conditions this idea can be generalized to find…