# 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