Extremal graphs for intersecting triangles
A \(k\)-fan is a graph with \(2k+ 1\) vertices consisting of \(k\) 3-cycles having one vertex in common. The authors show that if \(n\geq 50k^2\) and the graph \(G_n\) has more than \([n^2/4]+ k^2- ck\) edges, where \(c\) equals 1 or 3/2 according as \(k\) is odd or even, then \(G_n\) contains a \(k\)-fan; furthermore, the bound for the number of edges is best possible.
scientific article; zbMATH DE number 767700