Open Problems


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Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0Topologyporton
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Inequality for square summable complex series Retkes✭✭1Analysistigris35711
Inequality of the means✭✭✭0Geometrymdevos
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Invariant subspace problem✭✭✭0Analysistchow
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
inverse of an integer matrixGregory✭✭0Algebralvoyster
Is every regular paratopological group Tychonoff?unknown✭✭0Topologyporton
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Graph Theory » Directed Graphsfhavet
Large induced forest in a planar graph.Abertson; Berman✭✭0Graph Theory » Topological G.T.fhavet
Length of surreal productGonshor1CombinatoricsLukáš Lánský
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Graph Theory » Coloring » Vertex coloringfhavet
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
Long directed cycles in diregular digraphsJackson✭✭✭0Graph Theory » Directed Graphsfhavet
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
Lovász Path Removal ConjectureLovasz✭✭0Graph Theoryfhavet
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
MacEachen ConjectureMcEachen1Number Theorybillymac00
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Matching cut and girth✭✭0Graph Theoryw
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Graph Theory » Basic G.T. » MatchingsJirka
Melnikov's valency-variety problemMelnikov0Graph Theory » Coloring » Vertex coloringasp
Middle levels problemErdos✭✭0Graph Theory » Basic G.T. » Cyclestchow
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0Graph Theoryfhavet
Mixing Circular ColouringsBrewster; Noel1Graph Theory » Coloring » Vertex coloringJon Noel
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Monochromatic empty triangles✭✭✭0Geometrymdevos
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