Abstract
In this paper, we show that, for p ⩾ 4, if E is a clique decomposition obtained by removing maximal cliques (i.e. their edges) of order at least p one by one until none remain, in which case the remaining edges are removed one by one, then the sum of the orders of the cliques in E is at most 2 t p−1 ( n). Here t p−1 ( n) denotes the number of edges in the Turán graph of order n which has no cliques of order p.
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