Komlós conjecture to Union-closed sets conjecture

• Komlós conjecture
• The linear arboricity conjecture
• Lovász's conjecture on Hamiltonian paths in vertex-transitive graphs (1970)
• The Lovász–Plummer conjecture (proved 2011) and Sheehan's conjecture
• Magic Squares
• Meyniel's conjecture on the cop number
• Ohba's conjecture (2002; proved by Noel, Reed and Wu 2015)
• Pebbling number conjecture
• The Petersen colouring conjecture (Jaeger 1988)
• Ramsey numbers
• The reconstruction conjecture
• Sidorenko's conjecture (1993)
• Six standard deviations suffice (Spencer's theorem)
• Snake in the box
• Sparse Ruler
• Steiner Systems
• Sumner's universal tournament conjecture (1971)
• The total colouring conjecture (Behzad 1965, Vizing 1968)
• Tuza's conjecture
• Union-closed sets conjecture

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