Open Problems


TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
Coloring the Odd Distance GraphRosenfeld✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Monotone 4-term Arithmetic ProgressionsDavis; Entringer; Graham; Simmons✭✭0Combinatoricsvjungic
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
Rota's basis conjectureRota✭✭✭0Combinatorics » Matricesmdevos
Even vs. odd latin squaresAlon; Tarsi✭✭✭0Combinatoricsmdevos
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
P vs. NPCook; Levin✭✭✭✭0Theoretical Comp. Sci. » Algorithmszitterbewegung
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Graph Theory » Infinite Graphsmdevos
Unfriendly partitionsCowan; Emerson✭✭✭0Graph Theory » Infinite Graphsmdevos
Strong matchings and coversAharoni✭✭✭0Graph Theory » Infinite Graphsmdevos
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
Equality in a matroidal circumference boundOxley; Royle✭✭0Combinatorics » Matroid TheoryGordon Royle
Ding's tau_r vs. tau conjectureDing✭✭✭0Combinatorics » Optimizationmdevos
Chords of longest cyclesThomassen✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Growth of finitely presented groupsAdyan✭✭✭0Group Theorymdevos
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
$C^r$ Stability ConjecturePalis; Smale✭✭✭✭0Analysism n
Seagull problemSeymour✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Chowla's cosine problemChowla✭✭✭0Number Theorymdevos
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
Combinatorial covering designsGordon; Mills; Rödl; Schönheim0Combinatorics » DesignsPseudonym
Partial List ColoringAlbertson; Grossman; Haas✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Cube-Simplex conjectureKalai✭✭✭0Geometry » Polytopesmdevos
Partial List ColoringIradmusa✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
Degenerate colorings of planar graphsBorodin✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Graph Theory » Basic G.T.mdevos
Edge Reconstruction ConjectureHarary✭✭✭0Graph Theorymelch
Hedetniemi's ConjectureHedetniemi✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Total Colouring ConjectureBehzad✭✭✭0Graph Theory » ColoringIradmusa
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
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
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Tarski's exponential function problemTarski✭✭0LogicCharles
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