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List edge colourings of some 1-factorable multigraphs. (English) Zbl 0860.05035
The list edge colouring conjecture asserts that, given any multigraph \(G\) with chromatic index \(k\), and any set system \(\{S_e:e\in E(G)\}\) with each \(|S_e|=k\), we can choose elements \(s_e\in S_e\) such that \(s_e\neq s_f\) whenever \(e\) and \(f\) are adjacent edges. Using a technique of Alon and Tarsi which involves the graph monomial \(\prod\{x_u-x_v: uv\in E\}\) of an oriented graph, this conjecture is verified for certain families of 1-factorable multigraphs, including 1-factorable planar graphs.

05C15 Coloring of graphs and hypergraphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C10 Planar graphs; geometric and topological aspects of graph theory
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