Abstract
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 .
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