3-list-coloring planar graphs of girth 4

In Thomassen (1995) 4], Thomassen proved that planar graphs of girth at least 5 are 3-choosable. In Li (2009) 3], Li improved Thomassen’s result by proving that planar graphs of girth 4 with no 4-cycle sharing a vertex with another 4- or 5-cycle are 3-choosable. In this paper, we prove that planar graphs of girth 4 with no 4-cycle sharing an edge with another 4- or 5-cycle are 3-choosable. It is clear that our result strengthens Li’s result.