Introduction to Graph Theory Book

  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