Chetwynd, Amanda G. and Hilton, A. J. W. (1990) *The chromatic index of graphs with large maximum degree, where the number of vertices of maximum degree is relatively small.* Journal of Combinatorial Theory, Series B, 48 (1). ISSN 0095-8956

## Abstract

By Vizing's theorem, the chromatic index χ′(G) of a simple graph G satisfies Δ(G) ≤ χ′(G) ≤ Δ(G) + 1; if χ′(G) = Δ(G), then G is Class 1, and if χ′(G) = Δ(G) + 1, then G is Class 2. We describe the structure of Class 2 graphs satisfying the inequality , where r is the number of vertices of maximum degree. A graph G is critical if G is Class 2 and χ′(H) < χ′(G) for all proper subgraphs H of G. We also describe the structure of critical graphs satisfying the inequality above. We also deduce, as a corollary, an earlier result of ours that a regular graph G of even order satisfying is Class 1.

Item Type: | Journal Article |
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Journal or Publication Title: | Journal of Combinatorial Theory, Series B |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics VC's Office |

ID Code: | 20024 |

Deposited By: | Prof Amanda Chetwynd |

Deposited On: | 25 Nov 2008 08:50 |

Refereed?: | No |

Published?: | Published |

Last Modified: | 01 Jan 2018 03:43 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/20024 |

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