Open Problems

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¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Woodall's ConjectureWoodall✭✭✭0Graph Theory » Directed Graphsmdevos
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Which outer reloids are equal to inner onesPorton✭✭0Topologyporton
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0Topologyrybu
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
What is the largest graph of positive curvature?DeVos; Mohar1Graph Theory » Topological G.T. » Planar graphsmdevos
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
What are hyperfuncoids isomorphic to?Porton✭✭0Topologyporton
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Weak saturation of the cube in the cliqueMorrison; Noel1Graph Theory » Extremal G.T.Jon Noel
Weak pentagon problemSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Waring rank of determinantTeitler✭✭0AlgebraZach Teitler
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Vertex Cover Integrality GapAtserias✭✭0Logic » Finite Model Theorydberwanger
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Graph TheoryIradmusa
Upgrading a completary multifuncoidPorton✭✭0Topologyporton
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Graph Theory » Infinite Graphsmdevos
Unit vector flowsJain✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Unfriendly partitionsCowan; Emerson✭✭✭0Graph Theory » Infinite Graphsmdevos
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
Turán Problem for $10$-Cycles in the HypercubeErdos✭✭0CombinatoricsJon Noel
Turán number of a finite family.Erdos; Simonovits✭✭0Graph Theoryfhavet
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Graph Theory » Extremal G.T.fhavet
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Transversal achievement game on a square gridErickson✭✭1CombinatoricsMartin Erickson
trace inequality✭✭0AlgebraMiwa Lin
Total Colouring ConjectureBehzad✭✭✭0Graph Theory » ColoringIradmusa
Three-chromatic (0,2)-graphsPayan✭✭0Graph Theory » ColoringGordon Royle
The Two Color ConjectureNeumann-Lara✭✭0Graph Theory » Directed Graphsmdevos
The three 4-flows conjectureDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Theory » Graph Algorithmsmdevos
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
The Riemann HypothesisRiemann✭✭✭✭0Number Theory » Analytic N.T.eric
The permanent conjectureKahn✭✭0Combinatorics » Matricesmdevos
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
The Double Cap ConjectureKalai✭✭0CombinatoricsJon Noel
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
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