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Edge-choosability of multicircuits. (English) Zbl 0928.05018
Author’s abstract: A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). The list-colouring conjecture (LCC) is that every multigraph \(G\) has edge-choosability (list chromatic index) \(\text{ch}'(G)\) equal to its chromatic index \(\chi '(G)\). In this paper the LCC is proved first for multicircuits, and then, building on results of Peterson and Woodall [cf. Zbl 0928.05012 above], for any multigraph \(G\) in which every block is bipartite or a multicircuit or has at most four vertices or has underlying simple graph of the form \(K_{1,1,p}\).

MSC:
05C15 Coloring of graphs and hypergraphs
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