A graph G is(d1,d2)-colorable if its vertex set can be partitioned into two sets V1 and V2 where the maximum degree of the graph induced by V1 and V2 is at most d1 and d2.By analyzing the structural properties of mini-mal counterexamples,it is proved that every graph with maximum average degree mad(G)＜37/12 is(2,4)-colorable by using discharging method.It is concluded that every planar graph with girth at least 6 is(2,4)-colorable.
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