Top Open Problems
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-3401 Strong edge colouring conjecture
- Math-3402 Cores of Cayley graphs
- Math-3403 Weak pentagon problem
- Math-3404 Algorithm for graph homomorphisms
- Math-3405 Real roots of the flow polynomial
- Math-3406 Circular flow number of regular class 1 graphs
- Math-3407 Coloring the Odd Distance Graph
- Math-3408 Hedetniemi's Conjecture
- Math-3409 Double-critical graph conjecture
- Math-3410 Are vertex minor closed classes chi-bounded?
- Math-3411 Choice Number of k-Chromatic Graphs of Bounded Order
- Math-3412 Erdős–Faber–Lovász conjecture
- Math-3413 Antidirected trees in digraphs
- Math-3414 Subdivision of a transitive tournament in digraphs with large outdegree.
- Math-3415 Hamilton cycle in small d-diregular graphs
- Math-3416 Erdős-Posa property for long directed cycles
- Math-3417 Monochromatic reachability in arc-colored digraphs
- Math-3418 Edge-disjoint Hamilton cycles in highly strongly connected tournaments.
- Math-3419 Partitionning a tournament into k-strongly connected subtournaments.
- Math-3420 Extremal problem on the number of tree endomorphism
- Math-3421 Odd-cycle transversal in triangle-free graphs
- Math-3422 Multicolour Erdős--Hajnal Conjecture
- Math-3423 PTAS for feedback arc set in tournaments
- Math-3424 ¿Are critical k-forests tight?
- Math-3425 Seymour's self-minor conjecture
- Math-3426 Unions of triangle free graphs
- Math-3427 Universal highly arc transitive digraphs
- Math-3428 Unfriendly partitions
- Math-3429 Highly arc transitive two ended digraphs
- Math-3430 End-Devouring Rays
- Math-3431 Grunbaum's Conjecture
- Math-3432 The Crossing Number of the Hypercube
- Math-3433 What is the largest graph of positive curvature?
- Math-3434 Subgroup formed by elements of order dividing n
- Math-3435 Burnside problem
- Math-3436 Termination of the sixth Goodstein Sequence
- Math-3437 Fixed-point logic with counting
- Math-3438 Order-invariant queries
- Math-3439 Blatter-Specker Theorem for ternary relations
- Math-3440 Finite entailment of Positive Horn logic
- Math-3441 MacEachen Conjecture
- Math-3442 A discrete iteration related to Pierce expansions
- Math-3443 Diophantine quintuple conjecture
- Math-3444 Lucas Numbers Modulo m
- Math-3445 Alexa's Conjecture on Primality
- Math-3446 The Erdos-Turan conjecture on additive bases
- Math-3447 Olson's Conjecture
- Math-3448 Sets with distinct subset sums
- Math-3449 Odd incongruent covering systems
- Math-3450 Covering systems with big moduli