Abstract

AbstractA classical theorem of Simonovits from the 1980s asserts that every graph satisfying must contain copies of . Recently, Morris and Saxton established a balanced version of Simonovits' theorem, showing that such has copies of , which are “uniformly distributed” over the edges of . Moreover, they used this result to obtain a sharp bound on the number of ‐free graphs via the method of hypergraph containers. In this article, we generalise Morris–Saxton's results for even cycles to ‐graphs. We also prove analogous results for complete ‐partite ‐graphs.

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