Planar graphs with cycles of length neither 4 nor 6 are (2,0,0)(2,0,0)-colorable

• We study improper colorability of planar graphs.
• We show that every planar graph with cycles of length neither 4 nor 6 is (2,0,0)(2,0,0)-colorable.
• This was done by reducibility analysis together with discharging.

Let d1,d2,…,dkd1,d2,…,dk be k non-negative integers. A graph G   is (d1,d2,…,dk)(d1,d2,…,dk)-colorable, if the vertex set of G   can be partitioned into subsets V1,V2,…,VkV1,V2,…,Vk such that the graph G[Vi]G[Vi] induced by ViVi has maximum degree at most didi for i=1,2,…,ki=1,2,…,k. In this paper, we show that planar graphs with cycles of length neither 4 nor 6 are (2,0,0)(2,0,0)-colorable.