Modular decomposition is a technique at the crossroads of several domains of combinatorics which applies to many discrete structures such as graphs, 2-structures, hypergraphs.Expand

We show how to label the nodes of every interval graphs of diameter D with integers of size [log- D ] + 1 bits so that the distance up to an additive factor 1 between two distinct nodes can be computed in constant time from their labels only.Expand

We revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses, namely the cographs and the 3-leaf power graphs.Expand

We consider small world graphs as defined by Kleinberg (2000), i.e., graphs obtained from a d-dimensional augmented meshes by adding links chosen at random according to the d-harmonic distribution.Expand

In this article, we link abstract and explicit networks through their combinatorial properties, by introducing the unrooted analog of level-k networks.Expand

We give a O(n+mlogn) algorithm for transitive orientation of a comparability graph, and simple linear algorithms to recognize interval graphs, convex graphs, Y-semichordal graphs and matrices that have consecutive ones property.Expand

We present an algorithm with runtime $O(k^{2k}n^3m) for the k-Interval Completion problem of deciding whether a graph on n vertices and m edges can be made into an interval graph by adding at most k edges.Expand

We characterize a class of signed permutations for which one can compute in polynomial time a reversal scenario that conserves all common intervals, and that is parsimonious among such scenarios.Expand