Open Problems


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Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Graph Theory » Basic G.T.mdevos
Edge Reconstruction ConjectureHarary✭✭✭0Graph Theorymelch
Hedetniemi's ConjectureHedetniemi✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Total Colouring ConjectureBehzad✭✭✭0Graph Theory » ColoringIradmusa
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Simplexity of the n-cube✭✭✭1Geometrymdevos
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner
Inequality of the means✭✭✭0Geometrymdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Graph TheoryVadim Lioubimov
Are different notions of the crossing number the same?Pach; Tóth✭✭✭0Graph Theory » Topological G.T. » Crossing numberscibulka
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Shuffle-Exchange ConjectureBeneš; Folklore; Stone✭✭✭0CombinatoricsVadim Lioubimov
Beneš ConjectureBeneš✭✭✭0CombinatoricsVadim Lioubimov
Beneš Conjecture (graph-theoretic form)Beneš✭✭✭0Graph TheoryVadim Lioubimov
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Graph TheoryIradmusa
Euler-Mascheroni constant✭✭✭0Number Theory » Analytic N.T.Juggernaut
Durer's ConjectureDurer; Shephard✭✭✭1Geometry » Polytopesdmoskovich
Oriented trees in n-chromatic digraphsBurr✭✭✭0Graph Theory » Directed Graphsfhavet
Decomposing an even tournament in directed paths.Alspach; Mason; Pullman✭✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Directed path of length twice the minimum outdegreeThomassé✭✭✭0Graph Theory » Directed Graphsfhavet
Ádám's ConjectureÁdám✭✭✭0Graph Theory » Directed Graphsfhavet
Splitting a digraph with minimum outdegree constraintsAlon✭✭✭0Graph Theory » Directed Graphsfhavet
Long directed cycles in diregular digraphsJackson✭✭✭0Graph Theory » Directed Graphsfhavet
Decomposing a connected graph into paths.Gallai✭✭✭0Graph Theory » Basic G.T. » Pathsfhavet
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