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Open Problems


TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
Length of surreal productGonshor✭1CombinatoricsLukáš Lánský
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
Convex uniform 5-polytopes✭✭1GeometryACW
Durer's ConjectureDurer; Shephard✭✭✭1Geometry » Polytopesdmoskovich
Mixing Circular ColouringsBrewster; Noel✭1Graph Theory » Coloring » Vertex coloringJon Noel
Inequality for square summable complex series Retkes✭✭1Analysistigris35711
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Earth-Moon ProblemRingel✭✭1Graph Theory » Coloring » Vertex coloringfhavet
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Choosability of Graph PowersNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Graph Theory » Basic G.T.mhaythorpe
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1Graph TheoryDavid Wood
Forcing a 2-regular minorReed; Wood✭✭1Graph Theory » Basic G.T. » MinorsDavid Wood
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
Chromatic number of associahedronFabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood✭✭1GeometryDavid Wood
Convex Equipartitions with Extreme PerimeterNandakumar✭✭1GeometryNandakumar
Weak saturation of the cube in the cliqueMorrison; Noel✭1Graph Theory » Extremal G.T.Jon Noel
Monochromatic vertex colorings inherited from Perfect Matchings✭✭✭1Graph TheoryMario Krenn
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
3-Edge-Coloring ConjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph 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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