Overview

This volume covers the principal branches of graph theory in more than a thousand exercises of varying complexity. Each section starts with the main definitions and a brief theoretical discussion, which will serve as a reminder when solving the problems. Answers and hints are supplied separately. Topics include trees, independence and coverings, matchings, tours, planarity, colourings, degree sequences, connectivity, digraphs and hypergraphs. This work is intended for researchers, lecturers and graduate students in graph theory, combinatorics, VLSI design, circuits and systems, and mathematical programming and optimization.

Full Product Details

Author:   O. Melnikov ,  V. Sarvanov ,  R.I. Tyshkevich ,  V. Yemelichev
Publisher:   Springer
Imprint:   Springer
Edition:   1998 ed.
Volume:   19
Dimensions:   Width: 15.60cm , Height: 2.00cm , Length: 23.40cm
Weight:   1.520kg
ISBN:  

9780792349068

ISBN 10:   0792349067
Pages:   356
Publication Date:   31 March 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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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