Introduction to Graph Theory

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