Results 1 
5 of
5
Modular Decomposition and Transitive Orientation
, 1999
"... A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular ..."
Abstract

Cited by 111 (12 self)
 Add to MetaCart
A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We give O(n +m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph. This gives linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparability graphs and their complements.
LexBFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing
, 2000
"... ..."
On Stable Cutsets in Graphs
, 2000
"... We answer a question of Corneil and Fonlupt by showing that deciding whether a graph has a stable cutset is NPcomplete even for restricted graph classes. Some efficiently solvable cases will be discussed, too. ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
We answer a question of Corneil and Fonlupt by showing that deciding whether a graph has a stable cutset is NPcomplete even for restricted graph classes. Some efficiently solvable cases will be discussed, too.
Divide and Conquer Revisited Application to Graph Algorithms
"... Abstract. Divideandconquer is a seminal paradigm of computer science that can be summarised as divide the problem into subproblems, conquer (solve) the subproblem and combine the partial solutions. Without any specic assumptions on the size of the subproblems, it enables to design quadratic time ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Divideandconquer is a seminal paradigm of computer science that can be summarised as divide the problem into subproblems, conquer (solve) the subproblem and combine the partial solutions. Without any specic assumptions on the size of the subproblems, it enables to design quadratic time worst case bound algorithms. Wellknown algorithms (e.g. median search [3]) propose to minimise the recursive computation in order to yield linear time. Up to our knowledge, no known method proposes to cut down the divideandcombine part. This paper show that doing so quadratic time can also be improved. As an example of application, the Common Connected Problem is considered (a problem arising from computational biology [2]). Given a pair of graphs G1 and G2 on the same vertex set V, it consists of nding the coarsest partition of V such that each part induces a connected subgraph of both G1 and G2. Using a divideandconquer approach, we propose a generic algorithm that, depending on the datastructure, can be used as well for arbitrary graphs, interval graphs and planar graphs. This algorithm equals the best known complexity bounds for the two former cases [6, 8] and improves the planar case by a log n factor. 1
decomposition and recognition
, 2003
"... www.elsevier.com/locate/dam A fully dynamic algorithm for modular ..."
(Show Context)