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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
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
Edge-Unfolding Convex PolyhedraShephard✭✭0GeometryErik Demaine
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
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 subgraphs✭0Graph TheoryAndrew King
Obstacle number of planar graphsAlpert; Koch; Laison✭1Graph 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
Lovász Path Removal ConjectureLovasz✭✭0Graph Theoryfhavet
Turán number of a finite family.Erdos; Simonovits✭✭0Graph Theoryfhavet
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Switching reconstruction of digraphsBondy; Mercier✭✭0Graph Theoryfhavet
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0Graph Theoryfhavet
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1Graph TheoryDavid Wood
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0Graph TheoryDavid Wood
Circular flow numbers of $r$-graphsSteffen✭✭0Graph TheoryEckhard Steffen
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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