Edge and Total Choosability of Near-Outerplanar Graphs

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) = (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 (

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Timothy J. Hetherington, Douglas R. Woodall
• Keywords: COMBINATORICS 2006, Incident Elements, K4-minor-free Graphs, Maximum Degree