Planar graphs without 4-cycles and intersecting triangles are (1,1,0)-colorable

Abstract For a set of nonnegative integers c 1 , … , c k , a ( c 1 , c 2 , … , c k ) -coloring of a graph G is a partition of V ( G ) into V 1 , … , V k such that for every i , 1 ≤ i ≤ k , G [ V i ] has maximum degree at most c i . In this paper, we prove that all planar graphs without 4-cycles and intersecting triangles are ( 1 , 1 , 0 ) -colorable.