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-1365 A homomorphism problem for flows
- Math-1366 Unit vector flows
- Math-1367 Antichains in the cycle continuous order
- Math-1368 Circular coloring triangle-free subcubic planar graphs
- Math-1369 Oriented chromatic number of planar graphs
- Math-1370 Coloring and immersion
- Math-1371 Counting 3-colorings of the hex lattice
- Math-1372 Circular colouring the orthogonality graph
- Math-1373 Mixing Circular Colourings
- Math-1374 Melnikov's valency-variety problem
- Math-1375 Weighted colouring of hexagonal graphs.
- Math-1376 Splitting a digraph with minimum outdegree constraints
- Math-1377 Cyclic spanning subdigraph with small cyclomatic number
- Math-1378 Complexity of the H-factor problem.
- Math-1379 Infinite uniquely hamiltonian graphs
- Math-1380 Hamiltonian cycles in line graphs of infinite graphs
- Math-1381 5-local-tensions
- Math-1382 Drawing disconnected graphs on surfaces
- Math-1383 Crossing sequences
- Math-1384 Linear Hypergraphs with Dimension 3
- Math-1385 Consecutive non-orientable embedding obstructions
- Math-1487 O3 — Finding a prime above a bound
- Math-1488 O4 — Finding a prime in an arithmetic progression
- Math-1489 O5b — Randomized polynomial-time integer factorization
- Math-1490 O6 — Factoring a positive-density set of integers
- Math-1491 O7a — Computing the squarefree part
- Math-1492 O7b — Factoring from a squarefree-part oracle
- Math-1493 O8 — Deterministic polynomial-time squarefreeness testing
- Math-1494 O10 — Factoring from roots modulo a composite
- Math-1495 O11a — Quadratic residuosity modulo a composite
- Math-1496 O11b — Factoring from composite quadratic residuosity
- Math-1497 O12 — Finding a quadratic nonresidue
- Math-1498 O13 — Realizing a prescribed quadratic signature
- Math-1499 O14 — Square roots modulo a prime
- Math-1500 O15 — Polynomial roots modulo a prime
- Math-1501 O16 — Factoring polynomials modulo a prime
- Math-1502 O17 — Constructing irreducible polynomials over finite fields
- Math-1503 O18a — Recognizing primitive roots deterministically
- Math-1504 O19 — Finding a primitive root modulo a prime
- Math-1505 O20 — Computing multiplicative orders modulo a prime
- Math-1506 O21 — Discrete logarithms modulo a prime
- Math-1507 O22b — Factoring from composite discrete logarithms
- Math-1508 O23 — Factoring from Euler's totient
- Math-1509 O25 — Solving binary quadratic congruences
- Math-1510 O26 — Discrete logarithm versus Diffie–Hellman key distribution
- Math-1511 O27 — Elliptic curves of prescribed order
- Math-1512 O28 — Discrete logarithms in elliptic-curve groups
- Math-1513 O30 — Polynomial-factor lattice approximation
- Math-1514 O31 — Order of a polynomial's Galois group
- Math-1515 O32 — Class numbers of imaginary quadratic orders