A graph G is called (k,d)* -choosable if, for every list assignment L satisfying |L(v)|=k for all v∈V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. Zhao and He first studied the (3,1)*-list coloring of the 2-connected planar graphs just by using Euler''s formula and the graph''s structural properties. The paper continues to investigate the use of Euler''s formula in (3,1)*-list coloring the planar graphs, and shows that Euler''s formula is also practicable in dealing with the planar graphs containing cut vertices.