In this paper, 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… (More)
We consider the problem of labeling the nodes of an n-node graph G with short labels in such a way that the distance between any two nodes u, v of G can be approximated efficiently (in constant time)… (More)
By making use of lexicographic breadth rst search (Lex-BFS) and partition re nement with pivots, we obtain very simple algorithms for some well-known problems in graph theory. We give a O(n + m log… (More)
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular… (More)
In the rst part of this paper, a new structure for chordal graph is introduced, namely the clique graph. This structure is shown to be optimal with regard to the set of clique trees. The greedy… (More)