Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Exponential Algorithms for KnapsackLipton✭✭1Theoretical Comp. Sci. » Algorithmsdick lipton
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
Average diameter of a bounded cell of a simple arrangementDeza; Terlaky; Zinchenko✭✭0Geometrydeza
Continous analogue of Hirsch conjectureDeza; Terlaky; Zinchenko✭✭0Geometry » Polytopesdeza
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
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
MSO alternation hierarchy over picturesGrandjean✭✭0Logic » Finite Model Theorydberwanger
Vertex Cover Integrality GapAtserias✭✭0Logic » Finite Model Theorydberwanger
Dividing up the unrestricted partitionsDavid S.; Newman✭✭0CombinatoricsDavidSNewman
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Big Line or Big Clique in Planar Point SetsKara; Por; Wood✭✭1GeometryDavid Wood
Book Thickness of SubdivisionsBlankenship; Oporowski✭✭1Graph TheoryDavid Wood
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Graph Theory » Topological G.T. » ColoringDavid Wood
Number of Cliques in Minor-Closed ClassesWood✭✭0Graph TheoryDavid Wood
Edge-Colouring Geometric Complete GraphsHurtado✭✭1GeometryDavid Wood
Partition of Complete Geometric Graph into Plane Trees✭✭0GeometryDavid Wood
Point sets with no empty pentagonWood1GeometryDavid Wood
Forcing a $K_6$-minorBarát ; Joret; Wood✭✭0Graph Theory » Basic G.T. » MinorsDavid Wood
Dirac's ConjectureDirac✭✭0GeometryDavid Wood
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1Graph TheoryDavid Wood
Forcing a 2-regular minorReed; Wood✭✭1Graph Theory » Basic G.T. » MinorsDavid Wood
General position subsetsGowers✭✭0GeometryDavid Wood
Nonrepetitive colourings of planar graphsAlon N.; Grytczuk J.; Hałuszczak M.; Riordan O.✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0Graph TheoryDavid Wood
Chromatic number of associahedronFabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood✭✭1GeometryDavid Wood
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
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Are different notions of the crossing number the same?Pach; Tóth✭✭✭0Graph Theory » Topological G.T. » Crossing numberscibulka
Separators in string graphsFox; Pach; Tóth✭✭0Graph Theorycibulka
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Tarski's exponential function problemTarski✭✭0LogicCharles
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
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