目次：ぱらぱらめくる『Introduction to Graph and Hypergraph Theory』

• 目次
  • I Graphs
  • II Hypergraphs
  • I Graphs
    • 1. Basic Definitions and Concepts
    • 2. Trees and Bipartite Graphs
    • 3. Chordal Graphs
    • 4. Planar Graphs
    • 5. Graph Coloring
    • 6. Traversals and Flows
  • II Hypergraphs
    • 7. Basic Hypergraph Concepts
    • 8. Hypertrees and Chordal Hypergraphs
    • 9. Some Other Remarkable Hypergraph Classes
    • 10. Hypergraph Coloring
    • 11. Modeling with Hypergraph
  • 12. Appendix
• 詳しい目次
  • I Graphs
    • 1. Basic Definitions and Concepts
      • Fundamentals
      • Graph Modeling Applications
      • Graph Representations
      • Generalizations
      • Basic Graph Classes
      • Basic Graph Operations
      • Basic Subgraphs
      • Separation and Connectivity
    • 2. Trees and Bipartite Graphs
      • Trees and Cycles
      • Trees and Distance
      • Minimum Spaninng Tree
      • Bipartite Graphs
    • 3. Chordal Graphs
      • Preliminary
      • Separators and Simplicial Vertices
      • Degrees
      • Distances in Chordal Graphs
      • Quasi-trinagulated Graphs
    • 4. Planar Graphs
      • Plane and Planar Graphs
      • Euler's FOrmula
      • K5 and K3.3 Are not Planar Graphs
      • Kuratowski's Tehorem and Planarity Testing
      • Plane Triangulations and Dual Graphs
    • 5. Graph Coloring
      • Preliminary
      • Definitions and Examples
      • Structure of Colorings
      • Chromatic Polynomial
      • Coloring Chordal Graphs
      • Coloring Planar Graphs
      • Perfect Graphs
      • Edge Coloring and Vizing's Theorem
      • Upper Chromatic Index
    • 6. Traversals and Flows
      • EulerGraphs
      • Hamiltonian Graphs
      • Network Flows
  • II Hypergraphs
    • 7. Basic Hypergraph Concepts
      • Preliminary Definitions
      • Incidence and Duality
      • Basic Hypergraph Classes
      • Basic Hypergraph Operations
      • Subhypergraphs
      • Conformality and Helly Property
    • 8. Hypertrees and Chordal Hypergraphs
      • Htpertrees and Chodal Conformal Hypergraphs
      • Algorithms on Hypertrees
      • Cyclomatic Nuber of a Hypergraph
    • 9. Some Other Remarkable Hypergraph Classes
      • Balanfed Hypergraphs
      • Interval Hypergraphs
      • Normal Hypergraphs
      • Planar Hypergraphs
    • 10. Hypergraph Coloring
      • Basic Kinds of Classic Hypergraph Coloring
      • Greedy Algorithm for the Lower Chromatic Number
      • Basic Definitions of Mixed Hypergraph Coloring
      • Greedy Algorithm for the Upper Chromatic Number
      • Splitting-Contraction Algorithm
      • Uncolorability
      • Unique Colorability
      • Perfection
      • Chromatic Spectrum
      • Cloring Planar Hypergraphs
    • 11. Modeling with Hypergraph
      • List Colorings without Lists
      • Resource Allocation
  • 12. Appendix
    • • What Is Mathematical Induction
      • Graph Theory Algorithms and Their Complexity
      • Answers and Hints to Selected Exercises
      • Glossary of Additional Concepts