Total choosability of planar graphs with maximum degree 4

Nicolas Roussel
2011 Discrete Applied Mathematics  
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 g ⩾ 6, 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.
doi:10.1016/j.dam.2010.10.001 fatcat:k3nxloju6vdqlos3hosfu7tjhm