Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates. Much care has been given to present the material at the most effective level for students taking a first course in graph theory. Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet accessible text that stimulates interest in an evolving subject and exploration in its many applications. This text is part of the "Walter Rudin Student" Series in Advanced Mathematics.
Sprache
Verlagsort
Verlagsgruppe
McGraw-Hill Education - Europe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Maße
Höhe: 238 mm
Breite: 165 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-07-320416-1 (9780073204161)
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Schweitzer Klassifikation
1 Introduction 1.1 Graphs and Graph Models 1.2 Connected Graphs 1.3 Common Classes of Graphs 1.4 Multigraphs and Digraphs 2 Degrees 2.1 The Degree of a Vertex 2.2 Regular Graphs 2.3 Degree Sequences 2.4 Excursion: Graphs and Matrices 2.5 Exploration: Irregular Graphs 3 Isomorphic Graphs 3.1 The Definition of Isomorphism 3.2 Isomorphism as a Relation 3.3 Excursion: Graphs and Groups 3.4 Excursion: Reconstruction and Solvability 4 Trees 4.1 Bridges 4.2 Trees 4.3 The Minimum Spanning Tree Problem 4.4 Excursion: The Number of Spanning Trees 5 Connectivity 5.1 Cut-Vertices 5.2 Blocks 5.3 Connectivity 5.4 Menger's Theorem 5.5 Exploration: Geodetic Sets 6 Traversability 6.1 Eulerian Graphs 6.2 Hamiltonian Graphs 6.3 Exploration: Hamiltonian Walks and Numbers 6.4 Excursion: The Early Books of Graph Theory 7 Digraphs 7.1 Strong Digraphs 7.2 Tournaments 7.3 Excursion: Decision-Making 7.4 Exploration: Wine Bottle Problems 8 Matchings and Factorization 8.1 Matchings 8.2 Factorization 8.3 Decompositions and Graceful Labelings 8.4 Excursion: Instant Insanity 8.5 Excursion: The Petersen Graph 8.6 Exploration: -Labeling of Graphs 9 Planarity 9.1 Planar Graphs 9.2 Embedding Graphs on Surfaces 9.3 Excursion: Graph Minors 9.4 Exploration: Embedding Graphs in Graphs 10 Coloring 10.1 The Four Color Problem 10.2 Vertex Coloring 10.3 Edge Coloring 10.4 Excursion: The Heawood Map Coloring Theorem 10.5 Exploration: Local Coloring 11 Ramsey Numbers 11.1 The Ramsey Number of Graphs 11.2 Turan's Theorem 11.3 Exploration: Rainbow Ramsey Numbers 11.4 Excursion: Erdos Numbers 12 Distance 12.1 The Center of a Graph 12.2 Distant Vertices 12.3 Excursion: Locating Numbers 12.4 Excursion: Detour and Directed Distance 12.5 Exploration: Channel Assignment 12.6 Exploration: Distance Between Graphs 13 Domination 13.1 The Domination Number of a Graph 13.2 Exploration: Stratification 13.3 Exploration: Lights Out 13.4 Excursion: And Still It Grows More Colorful Appendix 1 Sets and Logic Appendix 2 Equivalence Relations and Functions Appendix 3 Methods of Proof
