## Graph Edge Coloring: Vizing's Theorem and Goldberg's ConjectureFeatures recent advances and new applications in graph edge coloring Reviewing recent advances in the Edge Coloring Problem, The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explore important topics such as: -
Use of Tashkinov trees to obtain an asymptotic positive solution to Goldberg's conjecture -
Application of Vizing fans to obtain both known and new results -
Kierstead paths as an alternative to Vizing fans -
Classification problem of simple graphs -
Generalized edge coloring in which a color may appear more than once at a vertex
This book also features first-time English translations of two groundbreaking papers written by Vadim Vizing on an estimate of the chromatic class of a p-graph and the critical graphs within a given chromatic class. Written by leading experts who have reinvigorated research in the field, |

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### Contents

1 | |

Vizings Theorem and Goldbergs Conjecture 2 Vizing Fans | 19 |

Vizings Theorem and Goldbergs Conjecture 3 Kierstead Paths | 43 |

Vizings Theorem and Goldbergs Conjecture 4 Simple Graphs and Line Graphs | 51 |

Vizings Theorem and Goldbergs Conjecture 5 Tashkinov Trees | 115 |

Vizings Theorem and Goldbergs Conjecture 6 Goldbergs Conjecture | 155 |

Vizings Theorem and Goldbergs Conjecture 7 Extreme Graphs | 197 |

Vizings Theorem and Goldbergs Conjecture 8 Generalized Edge Colorings of Graphs | 213 |

Vizings Theorem and Goldbergs Conjecture 9 Twenty Pretty Edge Coloring Conjectures | 245 |

Vizings Theorem and Goldbergs Conjecture Appendix A Vizings Two Fundamental Papers | 269 |

Vizings Theorem and Goldbergs Conjecture Appendix B Fractional Edge Colorings | 281 |

Vizings Theorem and Goldbergs Conjecture References | 295 |

312 | |

314 | |

318 | |

### Other editions - View all

Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture Michael Stiebitz,Diego Scheide,Bjarne Toft,Lene M. Favrholdt No preview available - 2012 |