Let G be a planar graph with maximum degree 4. It is known that G is 8-totally choosable. It has been recently proved that if G has girth g6, then G is 5-totally choosable. In this note we improve the first result by showing that G is 7-totally choosable and complete the latter one by showing that G is 6-totally choosable if G has girth at least 5. © 2010 Elsevier B.V. All rights reserved.
Roussel, N. (2011). Total choosability of planar graphs with maximum degree 4. Discrete Applied Mathematics, 159(1), 87–89. https://doi.org/10.1016/j.dam.2010.10.001