Open Problems


TitleAuthor(s)sort iconImp.¹Rec.²Area » Topic » SubtopicPosted by
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
57-regular Moore graph?Hoffman; Singleton✭✭✭0Graph Theory » Algebraic G.T.mdevos
Edge-Colouring Geometric Complete GraphsHurtado✭✭1GeometryDavid Wood
Partial List ColoringIradmusa✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Graph TheoryIradmusa
Long directed cycles in diregular digraphsJackson✭✭✭0Graph Theory » Directed Graphsfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Graph Theory » Directed Graphsfhavet
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
A nowhere-zero point in a linear mappingJaeger✭✭✭0Combinatorics » Matricesmdevos
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
Unit vector flowsJain✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
The permanent conjectureKahn✭✭0Combinatorics » Matricesmdevos
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Cube-Simplex conjectureKalai✭✭✭0Geometry » Polytopesmdevos
The Double Cap ConjectureKalai✭✭0CombinatoricsJon Noel
Big Line or Big Clique in Planar Point SetsKara; Por; Wood✭✭1GeometryDavid Wood
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Graph Theory » Basic G.T. » Pathsfhavet
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
Complexity of the H-factor problem.Kühn; Osthus✭✭0Graph Theory » Extremal G.T.fhavet
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Graph Theory » Hypergraphsfhavet
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Stable set meeting all longest directed paths.Laborde; Payan; Xuong N.H.✭✭0Graph Theoryfhavet
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Exponential Algorithms for KnapsackLipton✭✭1Theoretical Comp. Sci. » Algorithmsdick lipton
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Graph Theory » Algebraic G.T.mdevos
Lovász Path Removal ConjectureLovasz✭✭0Graph Theoryfhavet
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Graph Theory » Directed Graphsfhavet
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Melnikov's valency-variety problemMelnikov0Graph Theory » Coloring » Vertex coloringasp
Syndicate content