**Introduction to Graphs**

Graphs and Subgraphs

Degree Sequences

Connected Graphs and Distance

Multigraphs and Digraphs

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**Trees and Connectivity**

Nonseparable Graphs

Trees

Spanning Trees

Connectivity and Edge-Connectivity

Menger’s Theorem

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**Eulerian and Hamiltonian Graphs**

Eulerian Graphs

Hamiltonian Graphs

Powers of Graphs and Line Graphs

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**Digraphs**

Strong Digraphs

Tournaments

Flows in Networks

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**Graphs: History and Symmetry **

Some Historical Figures of Graph Theory

The Automorphism Group of a Graph

Cayley Color Graphs

The Reconstruction Problem

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**Planar Graphs**

The Euler Identity

Planarity versus Nonplanarity

The Crossing Number of a Graph

Hamiltonian Planar Graphs

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**Graph Embeddings**

The Genus of a Graph

2-Cell Embeddings of Graphs

The Maximum Genus of a Graph

The Graph Minor Theorem

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**Vertex Colorings**

The Chromatic Number of a Graph

Color-Critical Graphs

Bounds for the Chromatic Number

Perfect Graphs

List Colorings

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**Map Colorings**

The Four Color Problem

Colorings of Planar Graphs

The Conjectures of Hajós and Hadwiger

Chromatic Polynomials

The Heawood Map-Coloring Problem

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**Matchings, Factorization, and Domination **

Matchings and Independence in Graphs

Factorization

Decomposition and Graceful Graphs

Domination

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**Edge Colorings**

Chromatic Index and Vizing’s Theorem

Class One and Class Two Graphs

Tait Colorings

Nowhere-Zero Flows

List Edge Colorings and Total Colorings

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**Extremal Graph Theory**

Turán’s Theorem

Cages

Ramsey Theory

**Hints and Solutions to Odd-Numbered Exercises**

Bibliography

Index of Names

Index of Mathematical Terms

List of Symbols