Open Problems


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Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
inverse of an integer matrixGregory✭✭0Algebralvoyster
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Invariant subspace problem✭✭✭0Analysistchow
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Infinite distributivity of meet over join for a principal funcoidPorton✭✭0Topologyporton
Inequality of the means✭✭✭0Geometrymdevos
Inequality for square summable complex series Retkes✭✭1Analysistigris35711
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0Topologyporton
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
Hedetniemi's ConjectureHedetniemi✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Graph Theory » Algebraic G.T.mdevos
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Graph Theory » Directed Graphsfhavet
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Growth of finitely presented groupsAdyan✭✭✭0Group Theorymdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Graphs of exact colorings✭✭0Algebrasabisood
Graph product of multifuncoidsPorton✭✭0Topologyporton
Graham's conjecture on tree reconstructionGraham✭✭0Graph Theory » Basic G.T.mdevos
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Graph Theory » Coloring » LabelingDOT
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Graph Theory » Basic G.T. » CyclesAgelos
Generalized path-connectedness in proximity spacesPorton✭✭0Topologyporton
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
General position subsetsGowers✭✭0GeometryDavid Wood
Gao's theorem for nonabelian groupsDeVos✭✭0Number Theory » Combinatorial N.T.mdevos
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
Fundamental group torsion for subsets of Euclidean 3-spaceAncient/folklore✭✭0Topologyrybu
Funcoidal products inside an inward reloidPorton✭✭0Topologyporton
Frobenius number of four or more integers✭✭1Number Theory » Combinatorial N.T.maxal
Friendly partitionsDeVos✭✭0Graph Theory » Basic G.T.mdevos
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1Graph TheoryDavid Wood
Forcing a 2-regular minorReed; Wood✭✭1Graph Theory » Basic G.T. » MinorsDavid Wood
Forcing a $K_6$-minorBarát ; Joret; Wood✭✭0Graph Theory » Basic G.T. » MinorsDavid Wood
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Finite Lattice Representation Problem✭✭✭✭0Algebrawilliamdemeo
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