## Chromatic Graph TheoryBeginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings. With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory. |

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### Contents

1 | |

Introduction to Graphs | 27 |

Trees and Connectivity | 53 |

Eulerian and Hamiltonian Graphs | 71 |

Matchings and Factorization | 91 |

Graph Embeddings | 109 |

Introduction to Vertex Colorings | 147 |

Bounds for the Chromatic Number | 175 |

Monochromatic and Rainbow Colorings | 289 |

Complete Colorings | 329 |

Distinguishing Colorings | 359 |

Colorings Distance and Domination | 397 |

Study Projects | 439 |

446 | |

Bibliography | 453 |

465 | |

Coloring Graphs on Surfaces | 205 |

Restricted Vertex Colorings | 223 |

Edge Colorings of Graphs | 249 |