Open Problems


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Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Olson's ConjectureOlson✭✭0Number Theory » Combinatorial N.T.mdevos
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Edge-antipodal colorings of cubesNorine✭✭0Combinatorics » Ramsey Theorymdevos
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Choosability of Graph PowersNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
The Two Color ConjectureNeumann-Lara✭✭0Graph Theory » Directed Graphsmdevos
Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
Convex Equipartitions with Extreme PerimeterNandakumar✭✭1GeometryNandakumar
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
Saturation in the HypercubeMorrison; Noel; Scott✭✭0CombinatoricsJon Noel
Extremal $4$-Neighbour Bootstrap Percolation in the HypercubeMorrison; Noel✭✭0CombinatoricsJon Noel
Weak saturation of the cube in the cliqueMorrison; Noel1Graph Theory » Extremal G.T.Jon Noel
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Circular choosability of planar graphsMohar0Graph Theory » Coloring » Homomorphismsrosskang
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Melnikov's valency-variety problemMelnikov0Graph Theory » Coloring » Vertex coloringasp
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Graph Theory » Directed Graphsfhavet
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Graph Theory » Algebraic G.T.mdevos
Lovász Path Removal ConjectureLovasz✭✭0Graph Theoryfhavet
Exponential Algorithms for KnapsackLipton✭✭1Theoretical Comp. Sci. » Algorithmsdick lipton
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
Stable set meeting all longest directed paths.Laborde; Payan; Xuong N.H.✭✭0Graph Theoryfhavet
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Complexity of the H-factor problem.Kühn; Osthus✭✭0Graph Theory » Extremal G.T.fhavet
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Graph Theory » Hypergraphsfhavet
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Graph Theory » Basic G.T. » Pathsfhavet
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
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