Star multigraphs with three vertices of maximum degree - Core

2 downloads 0 Views 907KB Size Report
Sep 30, 1985 - A conjecture formulated in [3] by Chetwynd and Hilton was: CONJECTURE 1. Let 1 < s < n. Let Gbea regular star multigraph on2n + 2 vertices ...
Math. Proe. Camb. Phil. Soc. (1986), 100, 303 Printed in Oreat Britain

303

Star multigraphs with three vertices of maximum degree B Y A. G. CHETWYND Department of Mathematics, University of Lancaster AND A. J. W. HILTON Department of Mathematics, University of Reading (Received 30 September 1985) 1. Introduction 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)^>-