A Class of Matchings and a Related Lattice

✍ Scribed by K. Kilakos

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 474 KB
• Volume: 66
• Category: Article
• ISSN: 0095-8956
• DOI: 10.1006/jctb.1996.0001

✦ Synopsis

Let '$(G) denote the fractional chromatic index of a graph G. Let M(G) be a family of matchings of G such that M # M(G) if and only if there exists a fractional '$(G)-edge colouring of G in which M is a colour class. We use Lova sz's matching lattice theorem to obtain a description of the lattice generated by M(G). We shall show that, in a sense, the only complication arises when G has the Petersen graph minus a vertex as a minor.