On the edge distribution in triangle-free graphs
Let \(G\) be a graph on \(n\) vertices. The author shows that if any subgraph of \(G\) induced by \(n/2\) vertices is of size at least \(n^ 2/36\) then \(G\) contains a triangle. Further, it is studied how much the edge distribution in a triangle-free graph deviates from the edge distribution in a typical random graph of the same order and size.
scientific article; zbMATH DE number 767693