Open Problems

TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Simplexity of the n-cube✭✭✭1Geometrymdevos
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
Inequality of the means✭✭✭0Geometrymdevos
Edge-Colouring Geometric Complete GraphsHurtado✭✭1GeometryDavid Wood
Partition of Complete Geometric Graph into Plane Trees✭✭0GeometryDavid Wood
Point sets with no empty pentagonWood1GeometryDavid Wood
Covering a square with unit squares✭✭0GeometryMartin Erickson
Convex uniform 5-polytopes✭✭1GeometryACW
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
Dirac's ConjectureDirac✭✭0GeometryDavid Wood
General position subsetsGowers✭✭0GeometryDavid Wood
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
Chromatic number of associahedronFabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood✭✭1GeometryDavid Wood
Convex Equipartitions with Extreme PerimeterNandakumar✭✭1GeometryNandakumar
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
Fat 4-polytopesEppstein; Kuperberg; Ziegler✭✭✭0Geometry » Polytopesmdevos
Continous analogue of Hirsch conjectureDeza; Terlaky; Zinchenko✭✭0Geometry » Polytopesdeza
Cube-Simplex conjectureKalai✭✭✭0Geometry » Polytopesmdevos
Extension complexity of (convex) polygons✭✭0Geometry » PolytopesDOT
Durer's ConjectureDurer; Shephard✭✭✭1Geometry » Polytopesdmoskovich
Pebbling a cartesian productGraham✭✭✭0Graph Theorymdevos
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
Edge Reconstruction ConjectureHarary✭✭✭0Graph Theorymelch
Book Thickness of SubdivisionsBlankenship; Oporowski✭✭1Graph TheoryDavid Wood
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Number of Cliques in Minor-Closed ClassesWood✭✭0Graph TheoryDavid Wood
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Graph TheoryVadim Lioubimov
Separators in string graphsFox; Pach; Tóth✭✭0Graph Theorycibulka
Odd cycles and low oddness✭✭0Graph TheoryGagik
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
Exact colorings of graphsErickson✭✭0Graph TheoryMartin Erickson
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Graph TheoryRobert Samal
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Graph TheoryRobert Samal
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Graph TheoryIradmusa
Covering powers of cycles with equivalence subgraphs0Graph TheoryAndrew King
Obstacle number of planar graphsAlpert; Koch; Laison1Graph TheoryAndrew King
Matching cut and girth✭✭0Graph Theoryw
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Graph TheoryAndrew King
Stable set meeting all longest directed paths.Laborde; Payan; Xuong N.H.✭✭0Graph Theoryfhavet
Arc-disjoint strongly connected spanning subdigraphsBang-Jensen; Yeo✭✭0Graph Theoryfhavet
Do any three longest paths in a connected graph have a vertex in common? Gallai✭✭0Graph Theoryfhavet
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