Every planar graph without cycles of length 4 or 9 is (1,1,0)-colorable

Let d1,d2,…,dk be k non-negative integers. A graph G is (d1,d2,…,dk)-colorable, if the vertex set of G can be partitioned into subsets V1,V2,…,Vk such that the subgraph G[Vi] induced by Vi has maximum degree at most di for i=1,2,…,k. In this paper, we prove that every planar graph without cycles of length 4 or 9 is (1,1,0)-colorable.