# Ramsey Theory

1. The Happy Ending problem: forcing convex polygons (Szekeres)
2. Forcing empty convex polygons
3. Does the Ramsey limit exist? What is the limit? ($100 /$250)
4. Constructive Ramsey ($100) 5. Lower bound for $$r(4, n)$$ ($250)
6. Lower bound for $$r(k, n)$$
7. Consecutive Ramsey numbers (Burr)
8. Bounds for growth of $$r(3, n)$$ (Sós) (two problems combined)
9. Linear Ramsey numbers (Burr) ($25) 10. Cliques are Ramsey-extremal (Graham) 11. $$r(G)$$ is subexponential in sqrt(edges) 12. $$r(G)$$ is bounded by $$r(\chi(G))$$ (1) 13. $$r(G)$$ is bounded by $$r(\chi(G))$$ (2) 14. Upper bound for Ramsey on trees (Burr) 15. Exact Ramsey value for some trees 16. Upper bound on r(tree, complete multi-partite) 17. Upper bound for Ramsey number for $$4$$-cycle 18. Exact values for Ramsey numbers for $$k$$-cycle (Faudree, Rousseau, Schelp) 19. Exact value for Ramsey number of $$k$$-cycle and star (Burr, Faudree, Rousseau, Schelp) 20. Upper bound for Ramsey number for the hypercube (Burr) 21. Multi-color Ramsey number for triangles ($250/$100) 22. $$r(3, 3, n)$$ is much larger than $$r(3, n)$$ 23. Multi-color Ramsey number for triangles grows faster than for other odd cycles (Graham) 24. Multi-color Ramsey number for even cycles (Graham) 25. $$3$$-color Ramsey number for $$n$$-cycles (Bondy) 26. Multi-color Ramsey number for trees (Graham) 27. Multi-color Ramsey number for complete bipartite graphs (Chung, Graham) 28. Size Ramsey number for graphs of bounded degree (Beck) 29. Size Ramsey number for complete balanced bipartite graphs (Faudree, Rousseau, Schelp) 30. Size Ramsey number for unions of stars (Burr, Faudree, Rousseau, Schelp) 31. A linear bound on some size Ramsey numbers (Faudree, Rousseau, Schelp) 32. A linear bound on some size Ramsey numbers for particular graphs (Faudree, Rousseau, Schelp) 33. A linear bound on some size Ramsey numbers for trees (Faudree, Rousseau, Schelp) 34. A linear bound on some size Ramsey numbers for odd cycles (Faudree, Rousseau, Schelp) 35. A linear bound on some size Ramsey numbers for cycles (Faudree, Rousseau, Schelp) 36. Upper bound on induced Ramsey numbers (Rödl) 37. Double exponential lower bound for $$3$$-uniform hypergraph Ramsey numbers (Hajnal, Rado) ($500)
38. Asymptotic behavior of $$t$$-uniform hypergraph Ramsey numbers (Hajnal, Rado)
39. Asymptotic behavior of generalized Ramsey numbers
40. Behavior of generalized hypergraph Ramsey numbers (\$500)