Open Problems

Titlesort iconAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted by
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
The circular embedding conjectureHaggard✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Graph TheoryAndrew King
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Graph Theory » Directed GraphsJS
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
The Alon-Tarsi basis conjectureAlon; Linial; Meshulam✭✭0Combinatorics » Matricesmdevos
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Termination of the sixth Goodstein SequenceGraham0Logicmdevos
Tarski's exponential function problemTarski✭✭0LogicCharles
Switching reconstruction of digraphsBondy; Mercier✭✭0Graph Theoryfhavet
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Sums of independent random variables with unbounded varianceFeige✭✭0Theoretical Comp. Sci.cwenner
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Subset-sums equality (pigeonhole version)✭✭✭0Theoretical Comp. Sci. » Complexitymdevos
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Subgraph of large average degree and large girth.Thomassen✭✭0Graph Theory » Basic G.T.fhavet
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Graph Theory » Directed Graphsfhavet
Sub-atomic product of funcoids is a categorical product✭✭0Algebraporton
Strong matchings and coversAharoni✭✭✭0Graph Theory » Infinite Graphsmdevos
Strong edge colouring conjectureErdos; Nesetril✭✭0Graph Theory » Coloring » Edge coloringfhavet
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Graph Theory » Coloring » Vertex coloringberger
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
Strict inequalities for products of filtersPorton0Topologyporton
Sticky Cantor sets✭✭0Topologyporton
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Graph TheoryRobert Samal
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Graph TheoryRobert Samal
Stable set meeting all longest directed paths.Laborde; Payan; Xuong N.H.✭✭0Graph Theoryfhavet
Square achievement game on an n x n gridErickson✭✭1CombinatoricsMartin Erickson
Splitting a digraph with minimum outdegree constraintsAlon✭✭✭0Graph Theory » Directed Graphsfhavet
Special PrimesGeorge BALAN1Number Theorymaththebalans
Something like Picard for 1-formsElsner✭✭0AnalysisMathOMan
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0Topologyrybu
Smooth 4-dimensional Poincare conjecturePoincare; Smale; Stallings✭✭✭✭0Topologyrybu
Slice-ribbon problemFox✭✭✭✭0Topologyrybu
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Graph Theory » Hypergraphsfhavet
Simplexity of the n-cube✭✭✭1Geometrymdevos
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Sidorenko's ConjectureSidorenko✭✭✭0Graph TheoryJon Noel
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Graph TheoryVadim Lioubimov
Shuffle-Exchange ConjectureBeneš; Folklore; Stone✭✭✭0CombinatoricsVadim Lioubimov
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Syndicate content