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All Combinatorics

Open conjectures about counting, arrangement and discrete structure. Belongs here: unproved claims in combinatorics and graph theory. Does not belong here: settled combinatorial results, which are theorems.

1/3-2/3 Conjecture

Big-Line-Big-Clique Conjecture

Conway's Thrackle Conjecture

Cycle Double Cover Conjecture

Dittert Conjecture

Erdos-Faber-Lovasz Conjecture

Erdos-Gyarfas Conjecture

Erdos-Hajnal Conjecture

Gilbert-Pollak Conjecture

Goldberg-Seymour Conjecture

Hadamard Conjecture

Hadwiger Conjecture

Hedetniemi's Conjecture

Herzog-Schonheim Conjecture

Hirsch Conjecture

Kahn-Kalai Conjecture

Kalai's 3^d Conjecture

List Coloring Conjecture

Lonely Runner Conjecture

Lovasz Conjecture

Reconstruction Conjecture

Ringel-Kotzig Conjecture

Rota's Basis Conjecture

Ryser's Conjecture

Scholz Conjecture

Sidorenko's Conjecture

Singmaster's Conjecture

Total Coloring Conjecture

Tuza's Conjecture

Union-Closed Sets Conjecture

Vizing's Conjecture