Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Preface 1. Pure Mathematics Introduction Euclidean Geometry as Pure Mathematics Games Why Study Pure Mathematics? What's Coming Suggested Reading 2. Graphs Introduction Sets Paradox Graphs Graph diagrams Cautions Common Graphs Discovery Complements and Subgraphs Isomorphism Recognizing Isomorphic Graphs Semantics The Number of Graphs Having a Given nu Exercises Suggested Reading 3. Planar Graphs Introduction UG, K subscript 5, and the Jordan Curve Theorem Are there More Nonplanar Graphs? Expansions Kuratowski's Theorem Determining Whether a Graph is Planar or Nonplanar Exercises Suggested Reading 4. Euler's Formula Introduction Mathematical Induction Proof of Euler's Formula Some Consequences of Euler's Formula Algebraic Topology Exercises Suggested Reading 5. Platonic Graphs Introduction Proof of the Theorem History Exercises Suggested Reading 6. Coloring Chromatic Number Coloring Planar Graphs Proof of the Five Color Theorem Coloring Maps Exercises Suggested Reading 7. The Genus of a Graph Introduction The Genus of a Graph Euler's Second Formula Some Consequences Estimating the Genus of a Connected Graph g-Platonic Graphs The Heawood Coloring Theorem Exercises Suggested Reading 8. Euler Walks and Hamilton Walks Introduction Euler Walks Hamilton Walks Multigraphs The Königsberg Bridge Problem Exercises Suggested Reading Afterword Solutions to Selected Exercises Index Special symbols
Preface 1. Pure Mathematics Introduction Euclidean Geometry as Pure Mathematics Games Why Study Pure Mathematics? What's Coming Suggested Reading 2. Graphs Introduction Sets Paradox Graphs Graph diagrams Cautions Common Graphs Discovery Complements and Subgraphs Isomorphism Recognizing Isomorphic Graphs Semantics The Number of Graphs Having a Given nu Exercises Suggested Reading 3. Planar Graphs Introduction UG, K subscript 5, and the Jordan Curve Theorem Are there More Nonplanar Graphs? Expansions Kuratowski's Theorem Determining Whether a Graph is Planar or Nonplanar Exercises Suggested Reading 4. Euler's Formula Introduction Mathematical Induction Proof of Euler's Formula Some Consequences of Euler's Formula Algebraic Topology Exercises Suggested Reading 5. Platonic Graphs Introduction Proof of the Theorem History Exercises Suggested Reading 6. Coloring Chromatic Number Coloring Planar Graphs Proof of the Five Color Theorem Coloring Maps Exercises Suggested Reading 7. The Genus of a Graph Introduction The Genus of a Graph Euler's Second Formula Some Consequences Estimating the Genus of a Connected Graph g-Platonic Graphs The Heawood Coloring Theorem Exercises Suggested Reading 8. Euler Walks and Hamilton Walks Introduction Euler Walks Hamilton Walks Multigraphs The Königsberg Bridge Problem Exercises Suggested Reading Afterword Solutions to Selected Exercises Index Special symbols
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