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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.

MSC:
 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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References:
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