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Open Problems


TitleAuthor(s)Imp.¹sort iconRec.²Area » Topic » SubtopicPosted by
Odd incongruent covering systemsErdos; Selfridge✭✭✭0Number Theory » Combinatorial N.T.Robert Samal
Coloring and immersionAbu-Khzam; Langston✭✭✭1Graph Theory » Coloring » Vertex coloringmdevos
Davenport's constant✭✭✭0Number Theory » Combinatorial N.T.mdevos
Rendezvous on a lineAlpern✭✭✭0Unsortedmdevos
Pebbling a cartesian productGraham✭✭✭0Graph Theorymdevos
Coloring the Odd Distance GraphRosenfeld✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Even vs. odd latin squaresAlon; Tarsi✭✭✭0Combinatoricsmdevos
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
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
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
Seagull problemSeymour✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Chowla's cosine problemChowla✭✭✭0Number Theorymdevos
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
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Simplexity of the n-cube✭✭✭1Geometrymdevos
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner

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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