Random Graphs and Graph Enumeration

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1. At what density is the chromatic number of a random graph r?
2. Find the range of expected chromatic numbers for a random graph
3. Random graphs contain cubes (Bollobás)
4. Large independent sets in all large subgraphs of a random graph (Bollobás)
5. Covering a random graph with triangles (Spencer)
6. Avoiding anti-monotone graph properties in a random graph (Suen, Winkler)
7. Number of induced \(G\)-subgraphs in a given graph
8. Adding an edge to an extremal \(4\)-cycle-free graph gives two \(4\)-cycles (Siminovits)
9. Number of triangles in a multi-partite graph with large minimum degree (Bollobás, Szemerédi)
10. Number of graphs with a forbidden subgraph (Kleitman, Rothschild)
11. Regular induced subgraphs (Fajtlowicz, Staton)
12. Graphs with induced subgraphs of any number of edges (McKay) ($100)
13. Count the ways to add a K₄ (Tuza)
14. Number of triangle-free graphs
15. Number of pentagons in a triangle free graph
16. A conjecture of \(3\)-colored triangles in the complete graph (Sós)