Graph Theory : An Introductory Course / by Béla Bollobás
(Graduate Texts in Mathematics ; 63)
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York |
| 出版年 | 1979 |
| 本文言語 | 英語 |
| 大きさ | X, 180p. 80 illus : online resource |
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| 内容注記 | I Fundamentals 1. Definitions 2. Paths, Cycles and Trees 3. Hamilton Cycles and Euler Circuits 4. Planar Graphs 5. An Application of Euler Trails to Algebra Exercises Notes II Electrical Networks 1. Graphs and Electrical Networks 2. Squaring the Square 3. Vector Spaces and Matrices Associated with Graphs Exercises Notes III Flows, Connectivity and Matching 1. Flows in Directed Graphs 2. Connectivity and Menger’s Theorem 3. Matching 4. Tutte’s 1-Factor Theorem Exercises Notes IV Extremal Problems 1. Paths and Cycles 2. Complete Subgraphs 3. Hamilton Paths and Cycles 4. The Structure of Graphs Exercises Notes V Colouring 1. Vertex Colouring 2. Edge Colouring 3. Graphs on Surfaces Exercises Notes VI Ramsey Theory 1. The Fundamental Ramsey Theorems 2. Monochromatic Subgraphs 3. Ramsey Theorems in Algebra and Geometry 4. Subsequences Exercises Notes VII Random Graphs 1. Complete Subgraphs and Ramsey Numbers—The Use of the Expectation 2. Girth and Chromatic Number—Altering a Random Graph 3. Simple Properties of Almost All Graphs—The Basic Use of Probability 4. Almost Determined Variables—The Use of the Variance 5. Hamilton Cycles—The Use of Graph Theoretic Tools Exercises Notes VIII Graphs and Groups 1. Cayley and Schreier Diagrams 2. Applications of the Adjacency Matrix 3. Enumeration and Pólya’s Theorem Exercises Notes Index of Symbols |
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| 一般注記 | From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1 |
| 著者標目 | *Bollobás, Béla author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Combinatorics FREE:Mathematics FREE:Combinatorics |
| 分 類 | DC23:511.6 |
| 巻冊次 | ISBN:9781461299677 
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| ISBN | 9781461299677 |
| URL | http://dx.doi.org/10.1007/978-1-4612-9967-7 |
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