Star multigraphs with three vertices of maximum degree
نویسنده
چکیده
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 edgecolouring of a multigraph G is a map : 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 number, x'(G) of G is the least value of \&\ for which an edge-colouring of G exista. Generalizing a well-known theorem of Vizing [14], we showed in [6] that, for a star-multigraph G,
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