Book:Richard J. Trudeau/Dots and Lines

Subject Matter

 * Graph Theory

Contents

 * 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 $v$ ... Exercises ... Suggested Reading


 * 3. PLANAR GRAPHS
 * Introduction ... $UG$, $K_5$, 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 HAMILTONIAN WALKS
 * Introduction ... Euler Walks ... Hamilton Walks ... Multigraphs ... The Königsberg Bridge Problem ... Exercises ... Suggested Reading


 * Afterword


 * Index


 * Special symbols