{"product_id":"perfect-graphs-9780471489702","title":"Perfect Graphs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTaking a fresh approach to graph theory, this book surveys the latest research articles, highlighting the new directions and seminal results. It also emphasizes the links the subject has to other areas of mathematics and its applications. In particular, the links between perfect graphs and frequency assignment for telecommunications are discussed.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...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)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList 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.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402609697111,"sku":"9780471489702","price":188.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471489702.jpg?v=1730480948","url":"https:\/\/bookcurl.com\/products\/perfect-graphs-9780471489702","provider":"Book Curl","version":"1.0","type":"link"}