Jorge L. Ramírez-Alfonsín / Bruce A. Reed (Hgg.)

Perfect Graphs

Herausgegeben:Ramírez-Alfonsín, Jorge L.; Reed, Bruce A.

• Gebundenes Buch

Produktbeschreibung

Ein moderner Ansatz zur Diskussion der neuesten Entwicklungen der idealen Graphentheorie! Gestützt auf die wichtigsten Originalarbeiten erläutert der Autor gegenwärtige Forschungsaufgaben und die Verknüpfung zwischen idealen Graphen und anderen Gebieten der Mathematik. Dabei führt er auch fachübergreifende Beispiele an, u.a. die Anwendung idealer Graphen zur Frequenzzuordnung in der Nachrichtentechnik oder die semidefinite Programmierung. Nicht nur für Mathematiker, sondern auch für Informatiker und Kommunikationswissenschaftler interessant!

Produktdetails

• Wiley-Interscience Series in Discrete Mathematics and Optimization
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 386
• Erscheinungstermin: 28. November 2001
• Englisch
• Abmessung: 253mm x 174mm x 27mm
• Gewicht: 862g
• ISBN-13: 9780471489702
• ISBN-10: 0471489700
• Artikelnr.: 09739354

Autorenporträt

Jorge L. Ramírez-Alfonsín is the editor of Perfect Graphs, published by Wiley. Bruce Alan Reed FRSC is a Canadian mathematician and computer scientist, the Canada Research Chair in Graph Theory and a professor of computer science at McGill University. His research is primarily in graph theory.

Inhaltsangabe

List of Contributors. Preface. Acknowledgements. 1. Origins and Genesis (C.
Berge and J.L. Ramirez Alfonsin). Perfection. Communication Theory. The
Perfect Graph Conjecture. Shannon's Capacity. Translation of the
Halle-Wittenberg Proceedings. Indian Report. References. 2. From Conjecture
to Theorem (Bruce A Reed). Gallai's Graphs. The Perfect Graph Theorem. Some
Polyhedral Consequences. A Stronger Theorem. References. 3. A Translation
of Gallai's Paper: "Transitiv Orientierbare Graphen" (Frederic Maffray and
Myriam Preissmann). Introduction and Results. The Proofs of Theorems
(3.12), (3.15) and 3.16). The Proofs of (3.18) and (3.19). The Proofs of
(3.1.16). The Proofs of (3.1.17). Determination of all Irreducible Graphs.
Determination of the Irreducible Graphs. References. 4. Even Pairs (Hazel
Everett et al). Introduction. Even Pairs and Perfect Graphs. Perfectly
Contractile Graphs. Quasi-parity Graphs. Recent Progress. Odd Pairs.
References. 5. The P_4-Structure of Perfect Graphs (Stefan Hougardy).
Introduction. P_4-Stucture: Basics, Isomorphisms and Recognition. Modules,
h-Sets, Split Graphs and Unique P_4-Structure. The Semi-Strong perfect
Graph Theorem. The Structure of the P_4-Isomorphism Classes. Recognizing
P_4-Structure. The P_4-Structure of Minimally Imperfect Graphs. The Partner
Structure and Other Generalizations. P_3-Structure. References. 6.
Forbidding Holes and Antiholes (Ryan Hayward and Bruce A. Reed).
Introduction. Graphs with No Holes. Graphs with No Discs. Graphs with No
Long Holes. Balanced Matrices. Bipartitie Graphs with No Hole of Length 4k
+ 2. Graphs without Even Holes. -Perfect Graphs. Graphs without Odd Holes.
References. 7. Perfectly Orderable Graphs: A Survey (Chinh T Hoang).
Introduction. Classical Graphs. Minimal Nonperfectly Orderable Graphs.
Orientations. Generalizations of Triangulated Graphs. Generalizations of
Complements of Chordal Bipartitie Graphs. Other Classes of Perfectly
Orderable Graphs. Vertex Orderings. Generalizations of Perfectly Orderable
Graphs. Optimizing Perfectly Ordered Graphs. References. 8. Cutsets in
Perfect and Minimal Imperfect Graphs (Irena Rusu). Introduction. How Did It
Start? Main Results on Minimal Imperfect Graphs. Applications: Star
Cutsets. Applications: Clique and Multipartite Cutsets. Applications:
Stable Cutsets. Two (Resolved) Conjectures. The Connectivity of Minimal
Imperfect Graphs. Some (More) Problems. References. 9. Some Aspects of
Minimal Imperfect Graphs (Myriam Preissmann and Andras Sebo). Introduction.
Imperfect and Partitionable Graphs. Properties. Constructions. References.
10. Graph Imperfection and Channel Assignment (Colin McDiarmid).
Introduction. The Imperfection Ratio. An Alternative Definition. Further
Results and Questions. background on Channel Assignment. References. 11. A
Gentle Introduction to Semi-definite Programming (Bruce A. Reed).
Introduction. The Ellipsoid Method. Solving Semi-definite Programs.
Randomized Rounding and Derandomization. Approximating MAXCUT.
Approximating Bandwidth. Graph Colouring. 12. The Theta Body. References.
The Theta Body and Imperfection (F.B. Shepherd). Background and Overview.
Optimization, Convexity and Geometry. The Theta Body. Partitionable Graphs.
Perfect Graph Characterizations and a Continuous Perfect Graph Conjecture.
References. 13. Perfect Graphs and Graph Entropy (Gabor Simonyi).
Introduction. The Information-Theoretic Interpretation. Some Basic
Properties. Structural Theorems: Relation to Perfectness. Applications.
Generalizations. Graph Capacities and Other Related Functionals.
References. 14 A Bibliography on Perfect Graphs (Vaek Chvátal). Index.

Rezensionen

"...illuminates the relationships between perfect graph theory and other fields of scientific enquiry..." ( SciTech Book News , Vol. 26, No. 2, June 2002)