Abstract
Erdős et al. [6] asked for what values of k there is a sequence of graphs ( G n ) n ∞ = 1 such that G n has n vertices and independence number o( n), contains no K 4, and no k + 1 vertices have the same degree. In [6] it is proved that such a k has to be at least 4, but the problem whether any such k exists is left open. By making use of some graphs constructed by Bollobás and Erdős [3], we shall prove that for k = 5 (and so for k ⩾ 5) there is such a sequence ( G n ) n ∞ = 1.
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