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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
P vs. NPCook; Levin✭✭✭✭0Theoretical Comp. Sci. » Algorithmszitterbewegung
Waring rank of determinantTeitler✭✭0AlgebraZach Teitler
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
Finite Lattice Representation Problem✭✭✭✭0Algebrawilliamdemeo
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
Matching cut and girth✭✭0Graph Theoryw
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
Monotone 4-term Arithmetic ProgressionsDavis; Entringer; Graham; Simmons✭✭0Combinatoricsvjungic
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Graph TheoryVadim Lioubimov
Shuffle-Exchange ConjectureBeneš; Folklore; Stone✭✭✭0CombinatoricsVadim Lioubimov
Beneš ConjectureBeneš✭✭✭0CombinatoricsVadim Lioubimov
Beneš Conjecture (graph-theoretic form)Beneš✭✭✭0Graph TheoryVadim Lioubimov
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
KPZ Universality Conjecture✭✭✭0ProbabilityTomas Kojar
Inequality for square summable complex series Retkes✭✭1Analysistigris35711
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Graph Theory » Extremal G.T.shudeshijie
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Graphs of exact colorings✭✭0Algebrasabisood
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0Topologyrybu
Smooth 4-dimensional Poincare conjecturePoincare; Smale; Stallings✭✭✭✭0Topologyrybu
Slice-ribbon problemFox✭✭✭✭0Topologyrybu
Realisation problem for the space of knots in the 3-sphereBudney✭✭0Topologyrybu
Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0Topologyrybu
Fundamental group torsion for subsets of Euclidean 3-spaceAncient/folklore✭✭0Topologyrybu
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Circular choosability of planar graphsMohar✭0Graph Theory » Coloring » Homomorphismsrosskang

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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