Open Problems


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Does every odd number coprime to its Euler totient divide some Carmichael number?Michon✭✭1Number Theory » Computational N.T.maxal
Divisibility of central binomial coefficientsGraham✭✭1Number Theory » Combinatorial N.T.maxal
A sextic counterexample to Euler's sum of powers conjectureEuler✭✭1Number Theory » Computational N.T.maxal
Counterexamples to the Baillie-PSW primality test✭✭1Number Theory » Computational N.T.maxal
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Three-chromatic (0,2)-graphsPayan✭✭0Graph Theory » ColoringGordon Royle
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
Big Line or Big Clique in Planar Point SetsKara; Por; Wood✭✭1GeometryDavid Wood
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Graph Theory » Basic G.T. » MatchingsJirka
Average diameter of a bounded cell of a simple arrangementDeza; Terlaky; Zinchenko✭✭0Geometrydeza
Continous analogue of Hirsch conjectureDeza; Terlaky; Zinchenko✭✭0Geometry » Polytopesdeza
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Graph Theory » Directed GraphsJS
Monotone 4-term Arithmetic ProgressionsDavis; Entringer; Graham; Simmons✭✭0Combinatoricsvjungic
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
Equality in a matroidal circumference boundOxley; Royle✭✭0Combinatorics » Matroid TheoryGordon Royle
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Is every regular paratopological group Tychonoff?unknown✭✭0Topologyporton
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Complete bipartite subgraphs of perfect graphsFox✭✭0Graph Theory » Basic G.T.mdevos
Coloring random subgraphsBukh✭✭0Graph Theory » Probabilistic G.T.mdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Graph Theory » Coloringmdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Tarski's exponential function problemTarski✭✭0LogicCharles
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Compatible Matching ConjectureWood✭✭0Graph Theory » Topological G.T. » DrawingsRobert Samal
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Middle levels problemErdos✭✭0Graph Theory » Basic G.T. » Cyclestchow
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Edge-antipodal colorings of cubesNorine✭✭0Combinatorics » Ramsey Theorymdevos
trace inequality✭✭0AlgebraMiwa Lin
Diophantine quintuple conjecture✭✭1Number Theorymaxal
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Frobenius number of four or more integers✭✭1Number Theory » Combinatorial N.T.maxal
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
Book Thickness of SubdivisionsBlankenship; Oporowski✭✭1Graph TheoryDavid Wood
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Graph Theory » Topological G.T. » ColoringDavid Wood
Exponential Algorithms for KnapsackLipton✭✭1Theoretical Comp. Sci. » Algorithmsdick lipton
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