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Open Problems


TitleAuthor(s)sort iconImp.¹Rec.²Area » Topic » SubtopicPosted by
Decomposing eulerian graphs✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Subset-sums equality (pigeonhole version)✭✭✭0Theoretical Comp. Sci. » Complexitymdevos
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
The Crossing Number of the Complete Graph✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
Oriented chromatic number of planar graphs✭✭0Graph Theory » Coloring » Vertex coloringRobert Samal
Counterexamples to the Baillie-PSW primality test✭✭1Number Theory » Computational N.T.maxal
Davenport's constant✭✭✭0Number Theory » Combinatorial N.T.mdevos
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Simplexity of the n-cube✭✭✭1Geometrymdevos
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Monochromatic empty triangles✭✭✭0Geometrymdevos
trace inequality✭✭0AlgebraMiwa Lin
Diophantine quintuple conjecture✭✭1Number Theorymaxal
Frobenius number of four or more integers✭✭1Number Theory » Combinatorial N.T.maxal
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Inequality of the means✭✭✭0Geometrymdevos
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Partition of Complete Geometric Graph into Plane Trees✭✭0GeometryDavid Wood
Odd cycles and low oddness✭✭0Graph TheoryGagik
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
Finite Lattice Representation Problem✭✭✭✭0Algebrawilliamdemeo
Sticky Cantor sets✭✭0Topologyporton
Nonseparating planar continuum✭✭0Topologyporton
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
Covering powers of cycles with equivalence subgraphs✭0Graph TheoryAndrew King
Covering a square with unit squares✭✭0GeometryMartin Erickson
Euler-Mascheroni constant✭✭✭0Number Theory » Analytic N.T.Juggernaut
Extension complexity of (convex) polygons✭✭0Geometry » PolytopesDOT
Matching cut and girth✭✭0Graph Theoryw
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0Number Theoryprinceps
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
Convex uniform 5-polytopes✭✭1GeometryACW
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Sub-atomic product of funcoids is a categorical product✭✭0Algebraporton
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)✭✭✭✭0TopologyJailton Viana
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Graphs of exact colorings✭✭0Algebrasabisood
One-way functions exist✭✭✭✭0Theoretical Comp. Sci. » Complexityporton

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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