Critical star multigraphs.

Chetwynd, Amanda G. and Hilton, A. J. W. (1986) Critical star multigraphs. Graphs and Combinatorics, 2 (1). pp. 209-221. ISSN 0911-0119

Abstract

A star-multigraphG is a multigraph in which there is a vertexv + which is incident with each non-simple edge. It is critical if it is connected, Class 2 and(G\e) < (G) for eache E(G). We show that, ifG is any star multigraph, then(G) (G) + 1. We investigate the edge-chromatic class of star multigraphs with at most two vertices of maximum degree. We also obtain a number of results on critical star multigraphs. We shall make use of these results in later papers.