Total 4-Choosability of Series-Parallel Graphs

@article{Woodall2006Total4O,
  title={Total 4-Choosability of Series-Parallel Graphs},
  author={Douglas R. Woodall},
  journal={Electr. J. Comb.},
  year={2006},
  volume={13}
}
It is proved that, if G is a K4-minor-free graph with maximum degree 3, then G is totally 4-choosable; that is, if every element (vertex or edge) of G is assigned a list of 4 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… CONTINUE READING
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