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 language | English |
|---|---|
| Pages (from-to) | 209-217 |
| Number of pages | 9 |
| Journal | Ars Combinatoria |
| Volume | 60 |
| State | Published - Jul 2001 |