Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Cores of Cayley graphsSamal✭✭✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
The Crossing Number of the Complete Graph✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Barnette's ConjectureBarnette✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
Weak pentagon problemSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Odd incongruent covering systemsErdos; Selfridge✭✭✭0Number Theory » Combinatorial N.T.Robert Samal
Covering systems with big moduliErdos; Selfridge✭✭0Number Theory » Combinatorial N.T.Robert Samal
Oriented chromatic number of planar graphs✭✭0Graph Theory » Coloring » Vertex coloringRobert Samal
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Graph TheoryRobert Samal
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Graph TheoryRobert Samal
Circular choosability of planar graphsMohar0Graph Theory » Coloring » Homomorphismsrosskang
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0Topologyrybu
Smooth 4-dimensional Poincare conjecturePoincare; Smale; Stallings✭✭✭✭0Topologyrybu
Slice-ribbon problemFox✭✭✭✭0Topologyrybu
Realisation problem for the space of knots in the 3-sphereBudney✭✭0Topologyrybu
Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0Topologyrybu
Fundamental group torsion for subsets of Euclidean 3-spaceAncient/folklore✭✭0Topologyrybu
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
Graphs of exact colorings✭✭0Algebrasabisood
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Graph Theory » Extremal G.T.shudeshijie
Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Inequality for square summable complex series Retkes✭✭1Analysistigris35711
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
Syndicate content