Planar graphs without 5-cycles and intersecting triangles are (1, 1, 0)-colorable

A ( c 1 , c 2 , ? , c k ) -coloring of G is a mapping ? : V ( G ) ? { 1 , 2 , ? , k } such that for every i , 1 ? i ? k , G V i has maximum degree at most c i , where G V i denotes the subgraph induced by the vertices colored i . Borodin and Raspaud conjecture that every planar graph without 5-cycles and intersecting triangles is ( 0 , 0 , 0 ) -colorable. We prove in this paper that such graphs are ( 1 , 1 , 0 ) -colorable.