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|Additional Physical Format:||Print version:
Handbook of combinatorics. Volume 1
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
Ronald L Graham; Martin Grötschel; László Lovász
|Description:||1 online resource (1 volume (various pagings)) : illustrations|
|Contents:||Front Cover; Handbook of Combinatorics; Copyright Page; Table of Contents; Preface; List of Contributors; Part I: Structures; Session 1: Graphs; CHAPTER 1. Basic Graph Theory: Paths and Circuits; 1. Basic concepts; 2. Hamilton paths and circuits in graphs; 3. Hamilton paths and circuits in digraphs; 4. Fundamental parameters; 5. Fundamental classes of graphs and digraphs; 6. Special proof techniques for paths and circuits; 7. Lengths of circuits; 8. Packings and coverings by paths and circuits; References; CHAPTER 2. Connectivity and Network Flows; 1. Introduction, preliminaries. 2. Reachability3. Directed walks and paths of minimum cost; 4. Circulations and flows; 5. Minimum cost circulations and flows; 6. Trees and arborescences; 7. Higher connectivity; 8. Multicommodity flows and disjoint paths; References; CHAPTER 3. Matchings and Extensions; 1. Introduction and preliminaries; 2. Bipartite matching; 3. Nonbipartite matching; 4. Structure theory; 5. Weighted matchings and polyhedra; 6. Variations and extensions; 7. Determinants, permanents and Pfaffians; 8. Stable sets and claw free graphs; Acknowledgement; References. CHAPTER 4. Colouring, Stable Sets and Perfect GraphsList of books and surveys; 1. Basic definitions and motivation; 2. Constructions and examples; 3. Algorithmic aspects; 4. Upper and lower bounds for the chromatic number; 5. Colour-critical graphs; 6. Graphs on surfaces; 7. Stable sets; 8. Perfect graphs; 9. Edge-colourings; 10. Concluding remarks; Acknowledgement; References; APPENDIX TO CHAPTER 4. Nowhere-Zero Flows; 1. Introduction; 2. Group-valued flows; 3. Applications of Theorem 2.3; 4. Nowhere-zero 4-flows; 5. The 3-flow conjecture; 6. The 5-flow conjecture; References. CHAPTER 5. Embeddings and Minors1. Introduction; 2. Graphs in the plane; 3. Graphs on higher surfaces; 4. Graph minors; 5. Embeddings and well-quasi-orderings of graphs; References; CHAPTER 6. Random Graphs; 1. Introduction; 2. Evolving graphs; 3. Evolution --
Main epochs; 4. Phase transition; 5. Thresholds, threshold spectra and 0-1 laws; 6. Distributions; 7. Extreme characteristics; 8. Coloring; Appendix A. Quasi-random graphs; References; Session 2: Finite Sets and Relations; CHAPTER 7. Hypergraphs; 1. Hypergraphs and set systems; 2. Hypergraphs versus graphs. 3. Remarkable hypergraphs and min-max properties4. Stability, transversals and matchings; 5. Coloring problems; References; CHAPTER 8. Partially Ordered Sets; Introduction; 1. Notation and terminology; 2. Dilworth's theorem and the Greene-Kleitman theorem; 3. Kierstead's chain partitioning theorem; 4. Sperner's lemma and the cross cut conjecture; 5. Linear extensions and correlation; 6. Balancing pairs and the 1/3-2/3 conjecture; 7. Dimension and posets of bounded degree; 8. Interval orders and semiorders; 9. Degrees of freedom; 10. Dimension and planarity; 11. Regressions and monotone chains.
|Responsibility:||edited by R.L. Graham, M. Grötschel, L. Lovász.|