## Edge-colourings of graphs |

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### Contents

INTRODUCTION | 2 |

THE CHROMATIC INDEX | 21 |

The Theorems of Vizing and Shannon | 30 |

Copyright | |

16 other sections not shown

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### Common terms and phrases

1-factor analogue Beineke chromatic index chromatic number colour missing colour the edge colourable graphs complete bipartite graph complete graph connected graph Corollary 11.3 Critical Graph Conjecture cubic graph cubic map edge vw edges of G Exercise Figure Fiorini four-colour problem four-colour theorem girth g graph G graph obtained graph of class graph of order graph or multigraph Graph Theory graph with maximum graph with valency-list Hamiltonian circuits Hamiltonian graph Hilton interchange the colours Jakobsen Latin square least Let G line-graph lower bound matrix maximum valency multigraph with maximum N.L. Biggs number of edges number of vertices obtained from G odd circuit odd order p-critical p-valent graph permutation Petersen graph planar graph possible valency-list Proc R.J. Wilson regular graphs result of Theorem Shannon snarks subgraph of G Szekeres uniquely 3-colourable graph valency of G vertex vertex-critical vertices of G vertices of valency Vizing's Adjacency Lemma Vizing's Theorem Werra