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Open Problems


Titlesort iconAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted by
Subgraph of large average degree and large girth.Thomassen✭✭0Graph Theory » Basic G.T.fhavet
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Subset-sums equality (pigeonhole version)✭✭✭0Theoretical Comp. Sci. » Complexitymdevos
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Sums of independent random variables with unbounded varianceFeige✭✭0Theoretical Comp. Sci.cwenner
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Switching reconstruction of digraphsBondy; Mercier✭✭0Graph Theoryfhavet
Tarski's exponential function problemTarski✭✭0LogicCharles
Termination of the sixth Goodstein SequenceGraham✭0Logicmdevos
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
The Alon-Tarsi basis conjectureAlon; Linial; Meshulam✭✭0Combinatorics » Matricesmdevos
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Graph Theory » Directed GraphsJS
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Graph TheoryAndrew King
The circular embedding conjectureHaggard✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Graph✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Double Cap ConjectureKalai✭✭0CombinatoricsJon Noel
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
The permanent conjectureKahn✭✭0Combinatorics » Matricesmdevos
The Riemann HypothesisRiemann✭✭✭✭0Number Theory » Analytic N.T.eric
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Theory » Graph Algorithmsmdevos
The three 4-flows conjectureDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The Two Color ConjectureNeumann-Lara✭✭0Graph Theory » Directed Graphsmdevos
Three-chromatic (0,2)-graphsPayan✭✭0Graph Theory » ColoringGordon Royle
Total Colouring ConjectureBehzad✭✭✭0Graph Theory » ColoringIradmusa
trace inequality✭✭0AlgebraMiwa Lin
Transversal achievement game on a square gridErickson✭✭1CombinatoricsMartin Erickson
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Graph Theory » Extremal G.T.fhavet
Turán number of a finite family.Erdos; Simonovits✭✭0Graph Theoryfhavet
Turán Problem for $10$-Cycles in the HypercubeErdos✭✭0CombinatoricsJon Noel
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
Unfriendly partitionsCowan; Emerson✭✭✭0Graph Theory » Infinite Graphsmdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Unit vector flowsJain✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Graph Theory » Infinite Graphsmdevos
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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