Open Problems


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A diagram about funcoids and reloidsPorton✭✭0Topologyporton
Which outer reloids are equal to inner onesPorton✭✭0Topologyporton
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphsfhavet
Cycle Double Covers Containing Predefined 2-Regular SubgraphsArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Waring rank of determinantTeitler✭✭0AlgebraZach Teitler
Edge-Unfolding Convex PolyhedraShephard✭✭0GeometryErik Demaine
Sidorenko's ConjectureSidorenko✭✭✭0Graph TheoryJon Noel
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.Jon Noel
What is the largest graph of positive curvature?DeVos; Mohar1Graph Theory » Topological G.T. » Planar graphsmdevos
A conjecture on iterated circumcentresGoddyn✭✭1Geometrymdevos
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Graph Theory » Basic G.T. » CyclesAgelos
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
Coloring and immersionAbu-Khzam; Langston✭✭✭1Graph Theory » Coloring » Vertex coloringmdevos
Big Line or Big Clique in Planar Point SetsKara; Por; Wood✭✭1GeometryDavid Wood
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Graph Theory » Basic G.T. » MatchingsJirka
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
End-Devouring RaysGeorgakopoulos1Graph Theory » Infinite GraphsAgelos
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Simplexity of the n-cube✭✭✭1Geometrymdevos
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
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
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
Criterion for boundedness of power seriesRüdinger1Analysisandreasruedinger
Distribution and upper bound of mimic numbersBhattacharyya✭✭1Number Theory » Analytic N.T.facility_cttb@i...
Edge-Colouring Geometric Complete GraphsHurtado✭✭1GeometryDavid Wood
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
Sequence defined on multisetsErickson✭✭1CombinatoricsMartin Erickson
Square achievement game on an n x n gridErickson✭✭1CombinatoricsMartin Erickson
Transversal achievement game on a square gridErickson✭✭1CombinatoricsMartin Erickson
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Graph TheoryRobert Samal
Point sets with no empty pentagonWood1GeometryDavid Wood
Special PrimesGeorge BALAN1Number Theorymaththebalans
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Graph Theory » Extremal G.T.shudeshijie
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Graph TheoryIradmusa
Obstacle number of planar graphsAlpert; Koch; Laison1Graph TheoryAndrew King
Erdős–Straus conjectureErdos; Straus✭✭1Number TheoryACW
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Length of surreal productGonshor1CombinatoricsLukáš Lánský
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