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In 2002, Bollobás and Scott posed the following problem: for an integer and a graph G of m edges, what is the smallest f(k, m) such that V(G) can be partitioned into V1,…,Vk in which for all , where denotes the number of edges with both ends in ? In this paper, we solve this problem asymptotically by showing that . We also show that V(G)...
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