Planar graphs with cycles of length neither 4 nor 7 are (3,0,0)-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 1≤i≤k. It is known that planar graphs with cycles of length neither 4 nor k, k∈{5,6}, are (3,0,0)-colorable. In this paper, we show that planar graphs with cycles of length neither 4 nor 7 are also (3,0,0)-colorable.