The modular decomposition of a graph G = (V,E) does not contain prime modules if and only if G is a cograph, that is, if no quadruple of vertices induces a simple connected path P4. The cograph editing problem consists in inserting into and deleting from G a set F of edges so that H = (V,E4F) is a cograph and |F | is minimum. This NP-hard combinatorial optimization 1 ar X iv :1 70 2. 07 49 9v 1...

It is a common task in modern biology to analyze or reconstruct the relationship of different species. Since it is assumed that related species share a common ancestor species, many genes are shared between those. Two genes from different species are called orthologous, if they originate from the same gene in their common ancestor species. An orthology graph on a set of genes X is the graph wit...

An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. We prove that every acyclic coloring of a cograph is also a star coloring and give a linear-time algorithm for finding a...

Ordinary colourings of cographs are well understood; we focus on more general colourings, known as matrix partitions. We show that all matrix partition problems for cographs admit polynomial time algorithms and forbidden induced subgraph characterizations, even for the list version of the problems. Cographs are the largest natural class of graphs that have been shown to have this property. We b...

We design two incremental algorithms for computing an inclusion-minimal completion of arbitrary graph into a cograph. The first one is able to do so while providing additional property which crucial in practice obtain completions using as few edges possible : it compute minimum-cardinality the neighbourhood new vertex introduced at each step. It runs O(n+m′) time, where m′ number completed grap...