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A $(c_1,c_2,...,c_k)$-coloring of $G$ is a mapping$\varphi:V(G)\mapsto\{1,2,...,k\}$ such that for every $i,1 \leq i \leq k$,$G[V_i]$ has maximum degree at most $c_i$, where $G[V_i]$ denotes the subgraphinduced by the vertices colored $i$. Borodin and Raspaud conjecture that everyplanar 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.

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