Planar graphs without cycles of length 4 or 7 are (2, 0, 0)-colorable
Peipei Liu, Yingqian Wang · Scientia Sinica Mathematica · 2014
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 graph G[Vk] induced by Vi has maximum degree at most di for em= 1, 2,..., k. In this paper, we show that planar graphs without cycles of length 4 or 7 are (2, 0, 0)-colorable.