Chetwynd, Amanda G. and Hilton, A. J. W. (1986) *Star multigraphs with three vertices of maximum degree.* Mathematical Proceedings of the Cambridge Philosophical Society, 100 (2). pp. 303-317. ISSN 0305-0041

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## Abstract

The graphs we consider here are either simple graphs, that is they have no loops or multiple edges, or are multigraphs, that is they may have more than one edge joining a pair of vertices, but again have no loops. In particular we shall consider a special kind of multigraph, called a star-multigraph: this is a multigraph which contains a vertex v*, called the star-centre, which is incident with each non-simple edge. An edge-colouring of a multigraph G is a map ø: E(G)→, where is a set of colours and E(G) is the set of edges of G, such that no two edges receiving the same colour have a vertex in common. The chromatic index, or edge-chromatic numberχ′(G) of G is the least value of || for which an edge-colouring of G exists. Generalizing a well-known theorem of Vizing [14], we showed in [6] that, for a star-multigraph G, where Δ(G) denotes the maximum degree (that is, the maximum number of edges incident with a vertex) of G. Star-multigraphs for which χ′(G) = Δ(G) are said to be Class 1, and otherwise they are Class 2.

Item Type: | Article |
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Journal or Publication Title: | Mathematical Proceedings of the Cambridge Philosophical Society |

Additional Information: | http://journals.cambridge.org/action/displayJournal?jid=PSP The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 100 (2), pp 303-317 1986, © 1986 Cambridge University Press. |

Subjects: | ?? qa ?? |

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

ID Code: | 19968 |

Deposited By: | Prof Amanda Chetwynd |

Deposited On: | 21 Nov 2008 16:51 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 23 Mar 2017 21:50 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19968 |

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