Open Problems


TitleAuthor(s)Imp.¹sort iconRec.²Area » Topic » SubtopicPosted by
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Woodall's ConjectureWoodall✭✭✭0Graph Theory » Directed Graphsmdevos
The Crossing Number of the Complete Graph✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Fat 4-polytopesEppstein; Kuperberg; Ziegler✭✭✭0Geometry » Polytopesmdevos
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Reed's omega, delta, and chi conjectureReed✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
Bases of many weightsSchrijver; Seymour✭✭✭0Combinatorics » Matroid Theorymdevos
Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
Aharoni-Berger conjectureAharoni; Berger✭✭✭0Combinatorics » Matroid Theorymdevos
Barnette's ConjectureBarnette✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Sets with distinct subset sumsErdos✭✭✭0Number Theory » Combinatorial N.T.mdevos
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
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
Rota's basis conjectureRota✭✭✭0Combinatorics » Matricesmdevos
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
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