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A graph G is (a:b)-colorable if there exists an assignment of b-elementsubsets of {1,...,a} to vertices of G such that sets assigned to adjacentvertices are disjoint. We show that every planar graph without cycles of length4 or 5 is (11:3)-colorable, a weakening of recently disproved Steinberg'sconjecture. In particular, each such graph with n vertices has an independentset of size at least 3n/11.

Planar graphs without cycles of length 4 or 5 are (11:3)-colorable