Open Problems

TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Edge-antipodal colorings of cubesNorine✭✭0Combinatorics » Ramsey Theorymdevos
Termination of the sixth Goodstein SequenceGraham0Logicmdevos
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
trace inequality✭✭0AlgebraMiwa Lin
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Graph Theory » Algebraic G.T.mdevos
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
Sums of independent random variables with unbounded varianceFeige✭✭0Theoretical Comp. Sci.cwenner
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner
Inequality of the means✭✭✭0Geometrymdevos
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Graph Theory » Basic G.T.andreasruedinger
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Are vertex minor closed classes chi-bounded?Geelen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Domination in cubic graphsReed✭✭0Graph Theory » Basic G.T.mdevos
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Theory » Graph Algorithmsmdevos
Number of Cliques in Minor-Closed ClassesWood✭✭0Graph TheoryDavid Wood
Partition of Complete Geometric Graph into Plane Trees✭✭0GeometryDavid Wood
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Graph TheoryVadim Lioubimov
Are different notions of the crossing number the same?Pach; Tóth✭✭✭0Graph Theory » Topological G.T. » Crossing numberscibulka
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
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