Open Problems


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Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
Complexity of square-root sumGoemans✭✭0Theoretical Comp. Sci. » Complexityabie
A conjecture on iterated circumcentresGoddyn✭✭1Geometrymdevos
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Special PrimesGeorge BALAN1Number Theorymaththebalans
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Graph Theory » Basic G.T. » CyclesAgelos
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
End-Devouring RaysGeorgakopoulos1Graph Theory » Infinite GraphsAgelos
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Are vertex minor closed classes chi-bounded?Geelen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Do any three longest paths in a connected graph have a vertex in common? Gallai✭✭0Graph Theoryfhavet
Decomposing a connected graph into paths.Gallai✭✭✭0Graph Theory » Basic G.T. » Pathsfhavet
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Separators in string graphsFox; Pach; Tóth✭✭0Graph Theorycibulka
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
Complete bipartite subgraphs of perfect graphsFox✭✭0Graph Theory » Basic G.T.mdevos
Slice-ribbon problemFox✭✭✭✭0Topologyrybu
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Graph Theory » Coloring » Homomorphismsjfoniok
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Acyclic edge-colouringFiamcik✭✭0Graph Theory » Coloring » Edge coloringmdevos
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Graph Theory » Topological G.T. » ColoringDavid Wood
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
Sums of independent random variables with unbounded varianceFeige✭✭0Theoretical Comp. Sci.cwenner
Chromatic number of associahedronFabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood✭✭1GeometryDavid Wood
A sextic counterexample to Euler's sum of powers conjectureEuler✭✭1Number Theory » Computational N.T.maxal
Sequence defined on multisetsErickson✭✭1CombinatoricsMartin Erickson
Square achievement game on an n x n gridErickson✭✭1CombinatoricsMartin Erickson
Exact colorings of graphsErickson✭✭0Graph TheoryMartin Erickson
Transversal achievement game on a square gridErickson✭✭1CombinatoricsMartin Erickson
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Erdős–Straus conjectureErdos; Straus✭✭1Number TheoryACW
Turán number of a finite family.Erdos; Simonovits✭✭0Graph Theoryfhavet
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
Strong edge colouring conjectureErdos; Nesetril✭✭0Graph Theory » Coloring » Edge coloringfhavet
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.Jon Noel
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Odd-cycle transversal in triangle-free graphsErdos; Faudree; Pach; Spencer✭✭0Graph Theory » Extremal G.T.fhavet
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Diagonal Ramsey numbersErdos✭✭✭✭0Combinatorics » Ramsey Theorymdevos
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