The fine structure of octahedron-free graphs
Journal of Combinatorial Theory Series B
Set systems and families of permutations with small traces
European Journal of Combinatorics
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Let Ex(n, k, μ) denote the maximum number ofedges of an n-vertex graph in which every subgraph ofk vertices has at most μ edges. Here we summarize someknown results of the problem of determining Ex(n, k,μ), give simple proofs, and find some new estimates and extremalgraphs. Besides proving new results, one of our main aims is toshow how the classical Turáan theory can be applied to suchproblems. The case μ = $(^{k}_{2}) - 1$ is the famous result ofTuráan. © 1998 John Wiley & Sons, Inc. J. GraphTheory 29: 185207, 1998