Open Problems


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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
Upgrading a completary multifuncoidPorton✭✭0Topologyporton
Atomicity of the poset of completary multifuncoidsPorton✭✭0Topologyporton
Atomicity of the poset of multifuncoidsPorton✭✭0Topologyporton
Graph product of multifuncoidsPorton✭✭0Topologyporton
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0Number Theoryprinceps
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
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