Let G be a finite simple graph. A list assignment is a function on the vertices that associates a list of colors with each vertex. An L-coloring is a function that colors each vertex with one of the colors in the union of all lists of colors, such that the color of a vertex is in its list of colors and such that any two adjacent vertices have different colors. A graph is L-colorable if it admits an L-coloring. A graph is called k-choosable if it is L-colorable for every list assignment that has at least k colors for each vertex.

This short and nice paper uses combinatorial arguments to show that every planar graph without 4-cycles adjacent to triangles is 4-choosable. This is an improvement on a result by Lam et al. [1] showing that every planar graph without 4-cycles is 4-choosable.