| Major topic | Major results |
| Basic graph theory | The first theorem Characterization of trees Characterization of bipartite graphs |
| Classical Ramsey theory | Erdös-Szekeres Theorem (x2) Erdös' probabilistic lower bound Small Ramsey numbers |
| Extremal graph theory |
Turán's theorem Erdös-Simonovits-Stone theorem Kövari-Sós-Turán theorem |
| Graph Ramsey theory | Tree vs Clique (Chvatál) Disjoint triangles (Burr-Erdös-Spencer) Bounded maximum degree (Chvatál-Rödl-Szemerédi-Trotter) |
| Anti-Ramsey theory |
Canonical Ramsey theorem (Erdös-Rado) Lefman-Rödl theorem Graph Anti-Ramsey (Erdös-Simonovits-Sós) Constrained Coloring |
| Probabilistic methods |
Basic model (Erdös-Rényi) First and second moment methods High girth and chromatic number Random graphs and threshold phenomena Szemerédi regularity lemma Lovász local lemma |
| Number theory | Colored arithmetic progressions |
| Geometry | Large convex sets in arbitrary point sets |