extremal

bidden subgraph \(H\), what is the maximum number of edges in an \(n\)-vertex graph that does not contain \(H\)? (Turán's problem) What is the minimum number of edges needed to guarantee the presence of a certain substructure? Some classic questions include

of random graphs, many of which remain active areas of investigation and are central to current developments in extremal graph theory. Related keywords: extremal graphs, graph theory, combinatorics, Turán's theorem, bipartite graphs, graph extremal problems, gr