A simple linear time algorithm for cograph recognition

Authors:
Michel Habib;Christophe Paul
Affiliations:
CNRS, Université Montpellier 2, LIRMM, 161 rue Ada, 34392 Montpellier Cedex 2, France;CNRS, Université Montpellier 2, LIRMM, 161 rue Ada, 34392 Montpellier Cedex 2, France
Venue:
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Year:
2005

Citing 9
Cited 3

Three partition refinement algorithms

SIAM Journal on Computing
A tree representation for P4-sparse graphs

Discrete Applied Mathematics
Efficient parallel recognition algorithms of cographs and distance hereditary graphs

Discrete Applied Mathematics
Linear-time modular decomposition and efficient transitive orientation of comparability graphs

SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

Theoretical Computer Science
Robust algorithms for restricted domains

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A simple paradigm for graph recognition: application to cographs and distance hereditary graphs

Theoretical Computer Science
Efficient and practical algorithms for sequential modular decomposition

Journal of Algorithms
A New Linear Algorithm for Modular Decomposition

CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming

An improvement on the complexity of factoring read-once Boolean functions

Discrete Applied Mathematics
Efficient algorithms for Roman domination on some classes of graphs

Discrete Applied Mathematics
Linear-time certifying recognition algorithms and forbidden induced subgraphs

Nordic Journal of Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we describe a new simple linear time algorithm to recognize cographs. Cographs are exactly the P4-free graphs (where P4 denotes the path with 4 vertices). The recognition process works in two steps. First, we use partition refinement techniques to produce a factorizing permutation, i.e., an ordering of the vertices in which the strong modules appear consecutively. Then a very simple test algorithm is provided to check whether the given graph is a cograph, using a single sweep of the permutation obtained in the first step.