Open Problems

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Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Edge Reconstruction ConjectureHarary✭✭✭0Graph Theorymelch
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Graph Theory » Basic G.T.mhaythorpe
trace inequality✭✭0AlgebraMiwa Lin
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
Are there infinitely many counterexamples to the Goldbach Conjecture? Is it possible to find out?Nguyen0Logicnamducnguyen
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Is every regular paratopological group Tychonoff?unknown✭✭0Topologyporton
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Pseudodifference of filter objectsPorton✭✭0Unsortedporton
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Domain and image of inner reloidPorton✭✭0Topologyporton
Outer reloid of restricted funcoidPorton✭✭0Topologyporton
Sticky Cantor sets✭✭0Topologyporton
Nonseparating planar continuum✭✭0Topologyporton
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0Topologyporton
Strict inequalities for products of filtersPorton0Topologyporton
Distributivity of inward reloid over composition of funcoidsPorton✭✭0Topologyporton
Funcoidal products inside an inward reloidPorton✭✭0Topologyporton
Upgrading a completary multifuncoidPorton✭✭0Topologyporton
Atomicity of the poset of completary multifuncoidsPorton✭✭0Topologyporton
Atomicity of the poset of multifuncoidsPorton✭✭0Topologyporton
Graph product of multifuncoidsPorton✭✭0Topologyporton
Sub-atomic product of funcoids is a categorical product✭✭0Algebraporton
Distributivity of a lattice of funcoids is not provable without axiom of choicePorton0Topologyporton
Decomposition of completions of reloidsPorton✭✭0Topologyporton
Every metamonovalued funcoid is monovaluedPorton✭✭0Topologyporton
Every metamonovalued reloid is monovaluedPorton✭✭0Topologyporton
Generalized path-connectedness in proximity spacesPorton✭✭0Topologyporton
Direct proof of a theorem about compact funcoidsPorton✭✭0Topologyporton
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0Number Theoryprinceps
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Combinatorial covering designsGordon; Mills; Rödl; Schönheim0Combinatorics » DesignsPseudonym
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
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