Split decomposition and graph-labelled trees: Characterizations and fully dynamic algorithms for totally decomposable graphs

Authors:
Emeric Gioan;Christophe Paul
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 23
Cited 0

Distance-hereditary graphs

Journal of Combinatorial Theory Series B
Decomposition of perfect graphs

Journal of Combinatorial Theory Series B
Reducing prime graphs and recognizing circle graphs

Combinatorica
Completely separable graphs

Discrete Applied Mathematics - Computational combinatiorics
An O(n2) algorithm for undirected split decomposition

Journal of Algorithms
Fully dynamic algorithms for chordal graphs

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Parallel algorithms for hierarchical clustering and applications to split decomposition and parity graph recognition

Journal of Algorithms
A simple paradigm for graph recognition: application to cographs and distance hereditary graphs

Theoretical Computer Science
The Design and Analysis of Computer Algorithms

The Design and Analysis of Computer Algorithms
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs

SIAM Journal on Computing
On graph powers for leaf-labeled trees

Journal of Algorithms
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)

LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
A fully dynamic algorithm for modular decomposition and recognition of cographs

Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Rank-width and vertex-minors

Journal of Combinatorial Theory Series B
Lexbfs based recognition algorithms for cographs and related families

Lexbfs based recognition algorithms for cographs and related families
Fully dynamic recognition algorithm and certificate for directed cograph

Discrete Applied Mathematics
A note on computing set overlap classes

Information Processing Letters
Structure and linear time recognition of 3-leaf powers

Information Processing Letters
An optimal, edges-only fully dynamic algorithm for distance-hereditary graphs

STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A new approach to graph recognition and applications to distance-hereditary graphs

TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Dynamic distance hereditary graphs using split decomposition

ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Delta-confluent drawings

GD'05 Proceedings of the 13th international conference on Graph Drawing
Survey: A survey of the algorithmic aspects of modular decomposition

Computer Science Review

Quantified Score

Hi-index	0.04

Visualization

Abstract

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 graphs, and for two non-trivial subclasses, namely the cographs and the 3-leaf power graphs. Precisely, we give structural and incremental characterizations, leading to optimal fully dynamic recognition algorithms for vertex and edge modifications, for each of these classes. These results rely on the new combinatorial framework of graph-labelled trees used to represent the split decomposition of general graphs (and also the modular decomposition). The point of the paper is to use bijections between the aforementioned graph classes and graph-labelled trees whose nodes are labelled by cliques and stars. We mention that this bijective viewpoint yields directly an intersection model for the class of distance hereditary graphs.