{"product_id":"perfect-graphs-isbn-9780471489702","title":"Perfect Graphs","description":"The theory of perfect graphs was born out of a conjecture about graph colouring made by Claude Berge in 1960. That conjecture remains unsolved, but has generated an important area of research in combinatorics. This book:\u003cbr\u003e * Includes an introduction by Claude Berge, the founder of perfect graph theory\u003cbr\u003e \u003cbr\u003e * Discusses the most recent developments in the field of perfect graph theory\u003cbr\u003e \u003cbr\u003e * Provides a thorough historical overview of the subject\u003cbr\u003e \u003cbr\u003e * Internationally respected authors highlight the new directions, seminal results and the links the field has with other subjects\u003cbr\u003e \u003cbr\u003e * Discusses how semi-definite programming evolved out of perfect graph theory\u003cbr\u003e The early developments of the theory are included to lay the groundwork for the later chapters. The most recent developments of perfect graph theory are discussed in detail, highlighting seminal results, new directions, and links to other areas of mathematics and their applications. These applications include frequency assignment for telecommunication systems, integer programming and optimisation.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!  List of Contributors.\u003cbr\u003e \u003cbr\u003e Preface.\u003cbr\u003e \u003cbr\u003e Acknowledgements.\u003cbr\u003e \u003cbr\u003e 1. Origins and Genesis (C. Berge and J.L. Ramirez Alfonsin).\u003cbr\u003e \u003cbr\u003e Perfection.\u003cbr\u003e \u003cbr\u003e Communication Theory.\u003cbr\u003e \u003cbr\u003e The Perfect Graph Conjecture.\u003cbr\u003e \u003cbr\u003e Shannon's Capacity.\u003cbr\u003e \u003cbr\u003e Translation of the Halle-Wittenberg Proceedings.\u003cbr\u003e \u003cbr\u003e Indian Report.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 2. From Conjecture to Theorem (Bruce A Reed).\u003cbr\u003e \u003cbr\u003e Gallai's Graphs.\u003cbr\u003e \u003cbr\u003e The Perfect Graph Theorem.\u003cbr\u003e \u003cbr\u003e Some Polyhedral Consequences.\u003cbr\u003e \u003cbr\u003e A Stronger Theorem.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 3. A Translation of Gallai's Paper: \"Transitiv Orientierbare Graphen\" (Frederic Maffray and Myriam Preissmann).\u003cbr\u003e \u003cbr\u003e Introduction and Results.\u003cbr\u003e \u003cbr\u003e The Proofs of Theorems (3.12), (3.15) and 3.16).\u003cbr\u003e \u003cbr\u003e The Proofs of (3.18) and (3.19).\u003cbr\u003e \u003cbr\u003e The Proofs of (3.1.16).\u003cbr\u003e \u003cbr\u003e The Proofs of (3.1.17).\u003cbr\u003e \u003cbr\u003e Determination of all Irreducible Graphs.\u003cbr\u003e \u003cbr\u003e Determination of the Irreducible Graphs.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 4. Even Pairs (Hazel Everett et al).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e Even Pairs and Perfect Graphs.\u003cbr\u003e \u003cbr\u003e Perfectly Contractile Graphs.\u003cbr\u003e \u003cbr\u003e Quasi-parity Graphs.\u003cbr\u003e \u003cbr\u003e Recent Progress.\u003cbr\u003e \u003cbr\u003e Odd Pairs.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 5. The P_4-Structure of Perfect Graphs (Stefan Hougardy).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e P_4-Stucture: Basics, Isomorphisms and Recognition.\u003cbr\u003e \u003cbr\u003e Modules, h-Sets, Split Graphs and Unique P_4-Structure.\u003cbr\u003e \u003cbr\u003e The Semi-Strong perfect Graph Theorem.\u003cbr\u003e \u003cbr\u003e The Structure of the P_4-Isomorphism Classes.\u003cbr\u003e \u003cbr\u003e Recognizing P_4-Structure.\u003cbr\u003e \u003cbr\u003e The P_4-Structure of Minimally Imperfect Graphs.\u003cbr\u003e \u003cbr\u003e The Partner Structure and Other Generalizations.\u003cbr\u003e \u003cbr\u003e P_3-Structure.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 6. Forbidding Holes and Antiholes (Ryan Hayward and Bruce A. Reed).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e Graphs with No Holes.\u003cbr\u003e \u003cbr\u003e Graphs with No Discs.\u003cbr\u003e \u003cbr\u003e Graphs with No Long Holes.\u003cbr\u003e \u003cbr\u003e Balanced Matrices.\u003cbr\u003e \u003cbr\u003e Bipartitie Graphs with No Hole of Length 4k + 2.\u003cbr\u003e \u003cbr\u003e Graphs without Even Holes.\u003cbr\u003e \u003cbr\u003e -Perfect Graphs.\u003cbr\u003e \u003cbr\u003e Graphs without Odd Holes.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 7. Perfectly Orderable Graphs: A Survey (Chinh T Hoang).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e Classical Graphs.\u003cbr\u003e \u003cbr\u003e Minimal Nonperfectly Orderable Graphs.\u003cbr\u003e \u003cbr\u003e Orientations.\u003cbr\u003e \u003cbr\u003e Generalizations of Triangulated Graphs.\u003cbr\u003e \u003cbr\u003e Generalizations of Complements of Chordal Bipartitie Graphs.\u003cbr\u003e \u003cbr\u003e Other Classes of Perfectly Orderable Graphs.\u003cbr\u003e \u003cbr\u003e Vertex Orderings.\u003cbr\u003e \u003cbr\u003e Generalizations of Perfectly Orderable Graphs.\u003cbr\u003e \u003cbr\u003e Optimizing Perfectly Ordered Graphs.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 8. Cutsets in Perfect and Minimal Imperfect Graphs (Irena Rusu).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e How Did It Start?\u003cbr\u003e \u003cbr\u003e Main Results on Minimal Imperfect Graphs.\u003cbr\u003e \u003cbr\u003e Applications: Star Cutsets.\u003cbr\u003e \u003cbr\u003e Applications: Clique and Multipartite Cutsets.\u003cbr\u003e \u003cbr\u003e Applications: Stable Cutsets.\u003cbr\u003e \u003cbr\u003e Two (Resolved) Conjectures.\u003cbr\u003e \u003cbr\u003e The Connectivity of Minimal Imperfect Graphs.\u003cbr\u003e \u003cbr\u003e Some (More) Problems.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 9. Some Aspects of Minimal Imperfect Graphs (Myriam Preissmann and Andras Sebo).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e Imperfect and Partitionable Graphs.\u003cbr\u003e \u003cbr\u003e Properties.\u003cbr\u003e \u003cbr\u003e Constructions.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 10. Graph Imperfection and Channel Assignment (Colin McDiarmid).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e The Imperfection Ratio.\u003cbr\u003e \u003cbr\u003e An Alternative Definition.\u003cbr\u003e \u003cbr\u003e Further Results and Questions.\u003cbr\u003e \u003cbr\u003e background on Channel Assignment.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 11. A Gentle Introduction to Semi-definite Programming (Bruce A. Reed).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e The Ellipsoid Method.\u003cbr\u003e \u003cbr\u003e Solving Semi-definite Programs.\u003cbr\u003e \u003cbr\u003e Randomized Rounding and Derandomization.\u003cbr\u003e \u003cbr\u003e Approximating MAXCUT.\u003cbr\u003e \u003cbr\u003e Approximating Bandwidth.\u003cbr\u003e \u003cbr\u003e Graph Colouring.\u003cbr\u003e \u003cbr\u003e 12. The Theta Body.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e The Theta Body and Imperfection (F.B. Shepherd).\u003cbr\u003e \u003cbr\u003e Background and Overview.\u003cbr\u003e \u003cbr\u003e Optimization, Convexity and Geometry.\u003cbr\u003e \u003cbr\u003e The Theta Body.\u003cbr\u003e \u003cbr\u003e Partitionable Graphs.\u003cbr\u003e \u003cbr\u003e Perfect Graph Characterizations and a Continuous Perfect Graph Conjecture.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 13. Perfect Graphs and Graph Entropy (Gabor Simonyi).\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e The Information-Theoretic Interpretation.\u003cbr\u003e \u003cbr\u003e Some Basic Properties.\u003cbr\u003e \u003cbr\u003e Structural Theorems: Relation to Perfectness.\u003cbr\u003e \u003cbr\u003e Applications.\u003cbr\u003e \u003cbr\u003e Generalizations.\u003cbr\u003e \u003cbr\u003e Graph Capacities and Other Related Functionals.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e 14 A Bibliography on Perfect Graphs (Vaek Chvátal).\u003cbr\u003e \u003cbr\u003e Index.  \"...illuminates the relationships between perfect graph theory and other fields of scientific enquiry...\" (\u003ci\u003eSciTech Book News\u003c\/i\u003e, Vol. 26, No. 2, June 2002)  \u003cp\u003eJorge 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.   Perfect graph theory was born out of a conjecture about graph colouring made by Claude Berge in 1960. That conjecture remains unsolved, but it has generated an important area of research in combinatorics. In this first book on the subject, the authors bring together all the questions, methods and ideas of perfect graph theory, and highlight the new methods and applications generated by Berge's conjecture.\u003cbr\u003e * Discusses the most recent developments in the field of perfect graph theory.\u003cbr\u003e \u003cbr\u003e * Highlights applications in frequency assignments for telecommunications systems, integer programming and optimization.\u003cbr\u003e \u003cbr\u003e * Discusses how semi-definite programming evolved out of perfect graph theory.\u003cbr\u003e \u003cbr\u003e * Includes an introduction by Claude Berg.\u003cbr\u003e * Features internationally respected authors.\u003cbr\u003e Primarily of interest to researchers from mathematics, combinatorics, computer science and telecommunications, the book will also appeal to students of graph theory.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989764194533,"sku":"NP9780471489702","price":278.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471489702.jpg?v=1761785389","url":"https:\/\/k12savings.com\/products\/perfect-graphs-isbn-9780471489702","provider":"K12savings","version":"1.0","type":"link"}