Open Problems


TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
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
Friendly partitionsDeVos✭✭0Graph Theory » Basic G.T.mdevos
Shuffle-Exchange ConjectureBeneš; Folklore; Stone✭✭✭0CombinatoricsVadim Lioubimov
Separators in string graphsFox; Pach; Tóth✭✭0Graph Theorycibulka
Beneš ConjectureBeneš✭✭✭0CombinatoricsVadim Lioubimov
Odd cycles and low oddness✭✭0Graph TheoryGagik
Something like Picard for 1-formsElsner✭✭0AnalysisMathOMan
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Beneš Conjecture (graph-theoretic form)Beneš✭✭✭0Graph TheoryVadim Lioubimov
Approximation Ratio for Maximum Edge Disjoint Paths problemBentz✭✭0Graph Theoryjcmeyer
Approximation ratio for k-outerplanar graphsBentz✭✭0Graph Theoryjcmeyer
Finding k-edge-outerplanar graph embeddingsBentz✭✭0Graph Theoryjcmeyer
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
Dividing up the unrestricted partitionsDavid S.; Newman✭✭0CombinatoricsDavidSNewman
Exact colorings of graphsErickson✭✭0Graph TheoryMartin Erickson
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Graph Theory » Coloring » Homomorphismsjfoniok
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Graph TheoryRobert Samal
Outer reloid of restricted funcoidPorton✭✭0Topologyporton
Finite Lattice Representation Problem✭✭✭✭0Algebrawilliamdemeo
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
Sticky Cantor sets✭✭0Topologyporton
Nonseparating planar continuum✭✭0Topologyporton
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0Topologyporton
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Graph Theory » Coloring » LabelingDOT
Covering powers of cycles with equivalence subgraphs0Graph TheoryAndrew King
Covering a square with unit squares✭✭0GeometryMartin Erickson
Euler-Mascheroni constant✭✭✭0Number Theory » Analytic N.T.Juggernaut
Strict inequalities for products of filtersPorton0Topologyporton
Extension complexity of (convex) polygons✭✭0Geometry » PolytopesDOT
Matching cut and girth✭✭0Graph Theoryw
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
Funcoidal products inside an inward reloidPorton✭✭0Topologyporton
Forcing a $K_6$-minorBarát ; Joret; Wood✭✭0Graph Theory » Basic G.T. » MinorsDavid Wood
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