Star list chromatic number of planar subcubic graphs

A proper coloring of the vertices of a graph G is called a star-coloring if the union of every two color classes induces a star forest. The graph G is L-star-colorable if for a given list assignment L there is a star-coloring π such that π(v)∈L(v). If G is L-star-colorable for any list assignment L with |L(v)|≥k for all v∈V(G), then G is called k-star-choosable. The star list chromatic number of G, denoted by $chi_{s}^{l}(G)$ , is the smallest integer k such that G is k-star-choosable. In this paper, we prove that every planar subcubic graph is 6-star-choosable.