Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs

Authors:
Daniel Meister
Affiliations:
Theoretische Informatik, Bayerische Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
Venue:
Discrete Applied Mathematics
Year:
2005

Citing 34
Cited 8

Three partition refinement algorithms

SIAM Journal on Computing
An incremental linear-time algorithm for recognizing interval graphs

SIAM Journal on Computing
An optimal greedy heuristic to color interval graphs

Information Processing Letters
Domination on cocomparability graphs

SIAM Journal on Discrete Mathematics
An $0(n \log n)$ Algorithm for Bandwidth of Interval Graphs

SIAM Journal on Discrete Mathematics
Simple linear time recognition of unit interval graphs

Information Processing Letters
A linear-time algorithm for proper interval graph recognition

Information Processing Letters
Triangulating graphs without asteroidal triples

Discrete Applied Mathematics
Pathwidth, Bandwidth, and Completion Problems to Proper Interval Graphs with Small Cliques

SIAM Journal on Computing
Asteroidal Triple-Free Graphs

SIAM Journal on Discrete Mathematics
Software reliability via run-time result-checking

Journal of the ACM (JACM)
Characterizations and algorithmic applications of chordal graph embeddings

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Separability generalizes Dirac's theorem

Discrete Applied Mathematics
Graph classes: a survey

Graph classes: a survey
Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs

SIAM Journal on Computing
Modular decomposition and transitive orientation

Discrete Mathematics - Special issue on partial ordered sets
The ultimate interval graph recognition algorithm?

Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A wide-range efficient algorithm for minimal triangulation

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
LEDA: a platform for combinatorial and geometric computing

LEDA: a platform for combinatorial and geometric computing
Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

Theoretical Computer Science
A practical algorithm for making filled graphs minimal

Theoretical Computer Science
Minimal elimination ordering for graphs of bounded degree

Discrete Applied Mathematics
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs

SIAM Journal on Computing
On claw-free asteroidal triple-free graphs

Discrete Applied Mathematics
Certifying algorithms for recognizing interval graphs and permutation graphs

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimal Elimination of Planar Graphs

SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Minimal Elimination Ordering Inside a Given Chordal Graph

WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Maximum Cardinality Search for Computing Minimal Triangulations

WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximating the Bandwidth for Asteroidal Triple-Free Graphs

ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A linear time recognition algorithm for proper interval graphs

Information Processing Letters
Interval degree and bandwidth of a graph

Discrete Applied Mathematics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs

Discrete Applied Mathematics
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences

Hardness and approximation of minimum distortion embeddings

Information Processing Letters
Bandwidth of bipartite permutation graphs in polynomial time

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Treewidth and minimum fill-in on permutation graphs in linear time

Theoretical Computer Science
Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Survey: Certifying algorithms

Computer Science Review
A peep through the looking glass: articulation points in lattices

ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Triangulation and clique separator decomposition of claw-free graphs

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science

Quantified Score

Hi-index	0.05

Visualization

Abstract

A chordal graph H is a triangulation of a graph G if H is obtained by adding edges to G. If no proper subgraph of H is a triangulation of G we call H a minimal triangulation of G. We introduce a new LexBFS-like breadth-first-search algorithm min-LexBFS. We show that variants of min-LexBFS yield linear-time algorithms for computing minimal triangulations of AT-free claw-free graphs and co-comparability graphs. These triangulation algorithms are used to improve approximation algorithms for the bandwidth of AT-free claw-free and co-comparability graphs. We present a certifying recognition algorithm for proper interval graphs.