Critical star multigraphs
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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 andχ′(G\e) < χ′(G) for eache ∈ E(G). We show that, ifG is any star multigraph, thenχ′(G) ≦ Δ(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.
Keywords
Maximum Degree Critical Star
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