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. 303317. ISSN 03050041

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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 starmultigraph: this is a multigraph which contains a vertex v*, called the starcentre, which is incident with each nonsimple edge. An edgecolouring 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 edgechromatic numberχ′(G) of G is the least value of  for which an edgecolouring of G exists. Generalizing a wellknown theorem of Vizing [14], we showed in [6] that, for a starmultigraph G, where Δ(G) denotes the maximum degree (that is, the maximum number of edges incident with a vertex) of G. Starmultigraphs for which χ′(G) = Δ(G) are said to be Class 1, and otherwise they are Class 2.
Item Type:  Journal Article 

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 303317 1986, © 1986 Cambridge University Press. 
Uncontrolled Keywords:  /dk/atira/pure/researchoutput/libraryofcongress/qa 
Subjects:  
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:  20 Jan 2020 01:12 
URI:  https://eprints.lancs.ac.uk/id/eprint/19968 
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