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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Abstract
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 |
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Publication Title: | Electronic Journal of Combinatorics |
Creators: | Hetherington, T.J. and Woodall, D.R. |
Publisher: | International Press |
Date: | 2006 |
Volume: | 13 |
Number: | 98 |
Divisions: | Schools > School of Science and Technology |
Record created by: | EPrints Services |
Date Added: | 09 Oct 2015 09:54 |
Last Modified: | 19 Oct 2015 14:24 |
URI: | https://irep.ntu.ac.uk/id/eprint/4691 |
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