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A graph is called «-degenerate if each of its subgraphs has a vertex of degree at most n. For each n the Lick-White number of graph G is the fewest number of sets into which V(G) can be partitioned such that each set induces an «-degenerate graph. An upper bound is obtained for the Lick-White number of graphs with given clique number. A number of estimates are derived for the number of vertices in triangle-free graphs with prescribed Lick-White number. These results are used to give lowerdoi:10.1090/s0002-9939-1978-0476560-x fatcat:2t55rf2ccjeoplivx2yn6sn4wm