HETHERINGTON, T.J. and WOODALL, D.R., 2006. Edge and total choosability of near-outerplanar graphs. Electronic Journal of Combinatorics, 13 (98).
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It is proved that, if G is a K4-minor-free graph with maximum degree ∆ ≥ 4, then G is totally (∆ + 1)-choosable; that is, if every element (vertex or edge) of G is assigned a list of ∆ + 1 colours, then every element can be coloured with a colour from its own list in such a way that every two adjacent or incident elements are coloured with different colours. Together with other known results, this shows that the List-Total-Colouring Conjecture, that ch’’(G) = χ’(G) for every graph G, is true for all K4-minor-free graphs. The List-Edge-Colouring Conjecture is also known to be true for these graphs. As a fairly straightforward consequence, it is proved that both conjectures hold also for all K2,3-minor free graphs and all ( K2 + (K1 U K2))-minor-free graphs.
|Item Type:||Journal article|
|Publication Title:||Electronic Journal of Combinatorics|
|Creators:||Hetherington, T.J. and Woodall, D.R.|
|Divisions:||Schools > School of Science and Technology|
|Depositing User:||EPrints Services|
|Date Added:||09 Oct 2015 09:54|
|Last Modified:||19 Oct 2015 14:24|
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