New exact values of the maximum size of graphs free of topological complete subgraphs (Q870962)

A generalization of the famous extremal problem of Turán asks for determining the number ex\((n,p)\), the maximum number of edges of a graph of order \(n\) not containing a graph homeomorphic to the complete graph on \(p\) vertices. In this paper the exact values of ex\((n,p)\) are given for \((7n+7)/12\leq p<(12n+1)/3\), provided that \(n-p\geq 15.\) The corresponding extremal graphs are described as well.