Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Complexity of square-root sumGoemans✭✭0Theoretical Comp. Sci. » Complexityabie
Erdős–Straus conjectureErdos; Straus✭✭1Number TheoryACW
Convex uniform 5-polytopes✭✭1GeometryACW
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Graph Theory » Basic G.T. » CyclesAgelos
End-Devouring RaysGeorgakopoulos1Graph Theory » Infinite GraphsAgelos
Criterion for boundedness of power seriesRüdinger1Analysisandreasruedinger
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Graph Theory » Basic G.T.andreasruedinger
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Covering powers of cycles with equivalence subgraphs0Graph TheoryAndrew King
Obstacle number of planar graphsAlpert; Koch; Laison1Graph TheoryAndrew King
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Graph TheoryAndrew King
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Cycle Double Covers Containing Predefined 2-Regular SubgraphsArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Melnikov's valency-variety problemMelnikov0Graph Theory » Coloring » Vertex coloringasp
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Graph Theory » Coloring » Vertex coloringberger
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
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
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
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
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
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
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
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