Asymptotically good choice numbers of multigraphs

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Abstract

For loopless multigraphs G, the total choice number is asymptotically its fractional counterpart as the latter invariant tends to infinity. If G is embedded in the plane, then the edge-face and entire choice numbers exhibit the same "asymptotically good" behaviour. These results are based mainly on an analogous theorem of Kahn [5] for the list-chromatic index. Together with work of Kahn and others, our three results give a complete answer to a natural question: which of the seven invariants associated with list-colouring the nonempty subsets of {V, E, F} are asymptotically good?

Original languageEnglish
Pages (from-to)209-217
Number of pages9
JournalArs Combinatoria
Volume60
StatePublished - Jul 2001

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