Truncated-degree-choosability of planar graphs

Assume G is a graph and k is a positive integer. Let f: V (G) N be defined as f (v) =\k, dG (v) \. If G is f-choosable, then we say G is k-truncated-degree-choosable. It was proved in Zhou, Zhu, Zhu, Arc-weighted acyclic orientations and variations of degeneracy of graphs, arXiv: 2308. 15853 that there is a 3-connected non-complete planar graph that is not 7-truncated-degree-choosable, and every 3-connected non-complete planar graph is 16-truncated-degree-choosable. This paper improves the bounds, and proves that there is a 3-connected non-complete planar graph that is not 8-truncated-degree-choosable and every non-complete 3-connected planar graph is 12-truncated-degree-choosable.