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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Choosability of Graph PowersNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
The Double Cap ConjectureKalai✭✭0CombinatoricsJon Noel
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Saturation in the HypercubeMorrison; Noel; Scott✭✭0CombinatoricsJon Noel
Extremal $4$-Neighbour Bootstrap Percolation in the HypercubeMorrison; Noel✭✭0CombinatoricsJon Noel
Turán Problem for $10$-Cycles in the HypercubeErdos✭✭0CombinatoricsJon Noel
Weak saturation of the cube in the cliqueMorrison; Noel✭1Graph Theory » Extremal G.T.Jon Noel
Sidorenko's ConjectureSidorenko✭✭✭0Graph TheoryJon Noel
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.Jon Noel
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Graph Theory » Directed GraphsJS
Euler-Mascheroni constant✭✭✭0Number Theory » Analytic N.T.Juggernaut
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there infinite number of Mersenne Primes?✭✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Length of surreal productGonshor✭1CombinatoricsLukáš Lánský
inverse of an integer matrixGregory✭✭0Algebralvoyster
$C^r$ Stability ConjecturePalis; Smale✭✭✭✭0Analysism n
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
Monochromatic vertex colorings inherited from Perfect Matchings✭✭✭1Graph TheoryMario Krenn
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
Covering a square with unit squares✭✭0GeometryMartin Erickson
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Something like Picard for 1-formsElsner✭✭0AnalysisMathOMan
Special PrimesGeorge BALAN✭1Number Theorymaththebalans
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
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
5-flow conjectureTutte✭✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
4-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos

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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