List edge colourings of some 1-factorable multigraphs

Abstract

The List Edge Colouring Conjecture asserts that, given any multigraphG with chromatic indexk and any set system {S e :eE(G)} with each |S e |=k, we can choose elementss e S e such thats e s f whenevere andf are adjacent edges. Using a technique of Alon and Tarsi which involves the graph monomial\(\prod {\left\{ {xu - x_\upsilon :u\upsilon \in E} \right\}}\) of an oriented graph, we verify this conjecture for certain families of 1-factorable multigraphs, including 1-factorable planar graphs.

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Supported by the University Research Council of Vanderbilt University and NSERC Canada grants A5414 and A5499.

Supported by NSERC Canada grant A5499

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Ellingham, M.N., Goddyn, L. List edge colourings of some 1-factorable multigraphs. Combinatorica 16, 343–352 (1996). https://doi.org/10.1007/BF01261320

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Mathematics Subject Classification (1991)

  • 05C15
  • (05C70, 05C10)