Exercises in Graph Theory / by O. Melnikov, V. Sarvanov, R. Tyshkevich, V. Yemelichev, I. Zverovich
(Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series ; 19)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1998 |
| 本文言語 | 英語 |
| 大きさ | VIII, 356 p : online resource |
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| 内容注記 | 1 ABC of Graph Theory 2 Trees 3 Independence and Coverings 4 Connectivity 5 Matroids 6 Planarity 7 Graph Traversals 8 Degree Sequences 9 Graph Colorings 10 Directed Graphs 11 Hypergraphs Answers to Chapter 1: ABC of Graph Theory 1.1 Graphs: Basic Notions 1.2 Walks, Paths, Components 1.3 Subgraphs and Hereditary Properties of Graphs. Reconstructibility 1.4 Operations on Graphs 1.5 Matrices Associated with Graphs 1.6 Automorphism Group of Graph Answers to Chapter 2: Trees 2.1 Trees: Basic Notions 2.2 Skeletons and Spanning Trees Answers to Chapter 3: Independence and Coverings 3.1 Independent Vertex Sets and Cliques 3.2 Coverings 3.3 Dominating Sets 3.4 Matchings 3.5 Matchings in Bipartite Graphs Answers to Chapter 4: Connectivity 4.1 Biconnected Graphs and Biconnected Components 4.3 Cycles and Cuts Answers to Chapter 5: Matroids 5.1 Independence Systems 5.2 Matroids 5.3 Binary Matroids Answers to Chapter 6: Planarity 6.1 Embeddings of Graphs. Euler Formula 6.2 Plane Triangulation 6.3 Planarity Criteria 6.4 Duality and Planarity 6.5 Measures of Displanarity Answers to Chapter 7: Graph Traversals 7.1 Eulerian Graphs 7.2 Hamiltonian Graphs Answers to Chapter 8: Degree Sequences 8.1 Graphical Sequences 8.3 Split and Threshold Graphs 8.4 Degree Sets and Arity Partitions Answers to Chapter 9: Graph Colorings 9.1 Vertex Coloring 9.2 Chromatic Polynomial 9.3 Edge Coloring 9.4 Colorings of Planar Graphs 9.5 Perfect Graphs Answers to Chapter 10: Directed Graphs 10.1 Directed Graphs: Basic Notions 10.2 Reachability and Components 10.3 Matrices Associated with Digraph 10.4 Tours and Paths 10.5 Tournaments 10.6 Base and Kernel Answers to Chapter 11: Hypergraphs 11.1 Hypergraphs: Basic Notions 11.2 Hypergraph Realizations Notations |
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| 一般注記 | This book supplements the textbook of the authors" Lectures on Graph The ory" [6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of graphs. The exercises are grouped into eleven chapters and numerous sections accord ing to the topics of graph theory: paths, cycles, components, subgraphs, re constructibility, operations on graphs, graphs and matrices, trees, independence, matchings, coverings, connectivity, matroids, planarity, Eulerian and Hamiltonian graphs, degree sequences, colorings, digraphs, hypergraphs. Each section starts with main definitions and brief theoretical discussions. They constitute a minimal background, just a reminder, for solving the exercises. the presented facts and a more extended exposition may be found in Proofs of the mentioned textbook of the authors, as well as in many other books in graph theory. Most exercises are supplied with answers and hints. In many cases complete solutions are given. At the end of the book you may find the index of terms and the glossary of notations. The "Bibliography" list refers only to the books used by the authors during the preparation of the exercisebook. Clearly, it mentions only a fraction of available books in graph theory. The invention of the authors was also driven by numerous journal articles, which are impossible to list here |
| 著者標目 | *Melnikov, O. author Sarvanov, V. author Tyshkevich, R. author Yemelichev, V. author Zverovich, I. author SpringerLink (Online service) |
| 件 名 | LCSH:Engineering LCSH:Computer science -- Mathematics 全ての件名で検索 LCSH:Mathematical optimization LCSH:Combinatorics LCSH:Electrical engineering LCSH:Electronic circuits FREE:Engineering FREE:Circuits and Systems FREE:Combinatorics FREE:Discrete Mathematics in Computer Science FREE:Electrical Engineering FREE:Optimization |
| 分 類 | DC23:621.3815 |
| 巻冊次 | ISBN:9789401715140 
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| ISBN | 9789401715140 |
| URL | http://dx.doi.org/10.1007/978-94-017-1514-0 |
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