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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
MSO alternation hierarchy over picturesGrandjean✭✭0Logic » Finite Model Theorydberwanger
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Vertex Cover Integrality GapAtserias✭✭0Logic » Finite Model Theorydberwanger
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
Tarski's exponential function problemTarski✭✭0LogicCharles
Termination of the sixth Goodstein SequenceGraham✭0Logicmdevos
Growth of finitely presented groupsAdyan✭✭✭0Group Theorymdevos
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
What is the largest graph of positive curvature?DeVos; Mohar✭1Graph Theory » Topological G.T. » Planar graphsmdevos
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
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 Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Are different notions of the crossing number the same?Pach; Tóth✭✭✭0Graph Theory » Topological G.T. » Crossing numberscibulka
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
5-local-tensionsDeVos✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Degenerate colorings of planar graphsBorodin✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Graph Theory » Topological G.T. » ColoringDavid Wood
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Large induced forest in a planar graph.Abertson; Berman✭✭0Graph Theory » Topological G.T.fhavet
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Graph Theory » Topological G.T.fhavet
Coloring random subgraphsBukh✭✭0Graph Theory » Probabilistic G.T.mdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Chromatic number of random lifts of complete graphsAmit✭✭0Graph Theory » Probabilistic G.T.DOT
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
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
End-Devouring RaysGeorgakopoulos✭1Graph Theory » Infinite GraphsAgelos
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos

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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