Jeremy P. Spinrad

Graph classes: a survey

Preface 1. Basic Concepts 2. Perfection, Generalized Perfection, and Related Concepts 3. Cycles, Chords and Bridges 4. Models and Interactions 5. Vertex and Edge Orderings 6. Posets 7. Forbidden Subgraphs 8. Hypergraphs and Graphs 9. Matrices and Polyhedra 10. Distance Properties 11. Algebraic Compositions and Recursive Definitions 12. Decompositions and Cutsets 13. Threshold Graphs and Related Concepts 14. The Strong Perfect Graph Conjecture Appendix A. Recognition Appendix B. Containment Relationships Bibliography Index.

Modular decomposition and transitive orientation

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 linear-space 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. c 1999 Published by Elsevier Science B.V. All rights reserved

Efficient graph representations

Explanatory remarks Introduction Implicit representation Intersection and containment representations Real numbers in graph representations Classes which use global information Visibility graphs Intersection of graph classes Graph classes defined by forbidden subgraphs Chordal bipartite graphs Matrices Decomposition Elimination schemes Recognition algorithms Robust algorithms for optimization problems Characterization and construction Applications Glossary Survey of results on graph classes Bibliography Index.

Bipartite permutation graphs

This paper examines the class of bipartite permutation graphs. Two characterizations of graphs in this class are presented. These characterizations lead to a linear time recognition algorithm, and to polynomial time algorithms for a number of NP-complete problems when restricted to graphs in this class.

On Comparability and Permutation Graphs

This paper presents a technique for orienting a comparability graph transitively in

Scalar aggregation in inconsistent databases

O(n^2 )

Incremental modular decomposition

time. The best previous algorithm for this problem required

Doubly lexical ordering of dense 0–1 matrices

\Omega (n^3 )

Recognition of circle graphs

time. When combined with a result in [SP], we can recognize permutation graphs in

P 4 -trees and substitution decomposition

O(n^2 )