Graph theory
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-63 Hadwiger Conjecture
- Math-115 Erdős–Hajnal Conjecture
- Math-122 O5a — Deterministic polynomial-time integer factorization
- Math-162 Congruent number decision problem
- Math-224 The Hadwiger-Nelson Problem
- Math-269 Sidorenko's Conjecture for Bipartite Graphons
- Math-272 Zarankiewicz Problem for K_{t,t}-Free Bipartite Graphs
- Math-303 Tutte's 5-Flow Conjecture
- Math-324 Erdős Girth Conjecture
- Math-339 Reconstruction Conjecture
- Math-354 3-flow conjecture
- Math-366 Asymptotic Turan Numbers of Even Cycles
- Math-413 GNRS Conjecture
- Math-415 Frankl's Union-Closed Sets Conjecture
- Math-440 Hamiltonian paths and cycles in vertex transitive graphs
- Math-473 Existence of the Diagonal Ramsey Growth Limit
- Math-500 List edge-coloring conjecture
- Math-512 The Graceful Tree Conjecture
- Math-560 The Total Coloring Conjecture
- Math-599 Meyniel's Conjecture on Cop Number
- Math-600 Graph Coloring Game Monotonicity
- Math-601 Perfect 1-Factorization Conjecture
- Math-602 Earth-Moon Problem
- Math-603 Gyárfás-Sumner Conjecture
- Math-604 Albertson Conjecture
- Math-605 Conway's Thrackle Conjecture
- Math-606 Harborth's Conjecture
- Math-607 Negami's Conjecture
- Math-608 Turán's Brick Factory Problem
- Math-609 Guy's Crossing Number Conjecture
- Math-610 Universal Point Sets
- Math-611 Conference Graph Existence
- Math-612 Conway's 99-Graph Problem
- Math-613 Degree Diameter Problem
- Math-614 Moore Graph Existence
- Math-615 Barnette's Conjecture
- Math-616 Chvátal's Toughness Conjecture
- Math-617 Erdős-Gyárfás Conjecture
- Math-618 Linear Arboricity Conjecture
- Math-619 Cubic Graph Pathwidth
- Math-620 Snake-in-the-Box Problem
- Math-621 Sumner's Conjecture
- Math-622 Unfriendly Partition Conjecture
- Math-623 Vizing's Conjecture
- Math-624 Ryser's Conjecture
- Math-625 Second Neighborhood Problem
- Math-626 Woodall's Conjecture
- Math-660 Erdős Problem #62
- Math-663 Erdős Problem #74
- Math-664 Erdős Problem #80