Open Problems


TitleAuthor(s)Imp.¹sort iconRec.²Area » Topic » SubtopicPosted by
Cores of Cayley graphsSamal✭✭✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
5-flow conjectureTutte✭✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Cycle double cover conjectureSeymour; Szekeres✭✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Diagonal Ramsey numbersErdos✭✭✭✭0Combinatorics » Ramsey Theorymdevos
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
The Riemann HypothesisRiemann✭✭✭✭0Number Theory » Analytic N.T.eric
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
P vs. NPCook; Levin✭✭✭✭0Theoretical Comp. Sci. » Algorithmszitterbewegung
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
$C^r$ Stability ConjecturePalis; Smale✭✭✭✭0Analysism n
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0Topologyrybu
Smooth 4-dimensional Poincare conjecturePoincare; Smale; Stallings✭✭✭✭0Topologyrybu
Slice-ribbon problemFox✭✭✭✭0Topologyrybu
Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0Topologyrybu
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
Finite Lattice Representation Problem✭✭✭✭0Algebrawilliamdemeo
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
Caccetta-Häggkvist ConjectureCaccetta; Häggkvist✭✭✭✭0Graph Theory » Directed Graphsfhavet
Closing Lemma for Diffeomorphism (Dynamical Systems)Charles Pugh✭✭✭✭0TopologyJailton Viana
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)✭✭✭✭0TopologyJailton Viana
One-way functions exist✭✭✭✭0Theoretical Comp. Sci. » Complexityporton
Are there infinite number of Mersenne Primes?✭✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
4-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Bouchet's 6-flow conjectureBouchet✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The circular embedding conjectureHaggard✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Faithful cycle coversSeymour✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Decomposing eulerian graphs✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
A nowhere-zero point in a linear mappingJaeger✭✭✭0Combinatorics » Matricesmdevos
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
57-regular Moore graph?Hoffman; Singleton✭✭✭0Graph Theory » Algebraic G.T.mdevos
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Graph Theory » Algebraic G.T.mdevos
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
Subset-sums equality (pigeonhole version)✭✭✭0Theoretical Comp. Sci. » Complexitymdevos
Ryser's conjectureRyser✭✭✭0Graph Theory » Hypergraphsmdevos
Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Graph Theory » Coloring » Vertex coloringberger
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