Open Problems


Titlesort iconAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted by
Odd-cycle transversal in triangle-free graphsErdos; Faudree; Pach; Spencer✭✭0Graph Theory » Extremal G.T.fhavet
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Odd incongruent covering systemsErdos; Selfridge✭✭✭0Number Theory » Combinatorial N.T.Robert Samal
Odd cycles and low oddness✭✭0Graph TheoryGagik
Obstacle number of planar graphsAlpert; Koch; Laison1Graph TheoryAndrew King
Number of Cliques in Minor-Closed ClassesWood✭✭0Graph TheoryDavid Wood
Nonseparating planar continuum✭✭0Topologyporton
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Graph Theory » Basic G.T.mdevos
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.Jon Noel
MSO alternation hierarchy over picturesGrandjean✭✭0Logic » Finite Model Theorydberwanger
Monotone 4-term Arithmetic ProgressionsDavis; Entringer; Graham; Simmons✭✭0Combinatoricsvjungic
Monochromatic vertex colorings inherited from Perfect Matchings✭✭✭1Graph TheoryMario Krenn
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphsfhavet
Monochromatic empty triangles✭✭✭0Geometrymdevos
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Mixing Circular ColouringsBrewster; Noel1Graph Theory » Coloring » Vertex coloringJon Noel
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0Graph Theoryfhavet
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
Melnikov's valency-variety problemMelnikov0Graph Theory » Coloring » Vertex coloringasp
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Graph Theory » Basic G.T. » MatchingsJirka
Matching cut and girth✭✭0Graph Theoryw
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Lovász Path Removal ConjectureLovasz✭✭0Graph Theoryfhavet
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
Long directed cycles in diregular digraphsJackson✭✭✭0Graph Theory » Directed Graphsfhavet
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Length of surreal productGonshor1CombinatoricsLukáš Lánský
Large induced forest in a planar graph.Abertson; Berman✭✭0Graph Theory » Topological G.T.fhavet
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Graph Theory » Directed Graphsfhavet
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Syndicate content