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Open Problems


TitleAuthor(s)sort iconImp.¹Rec.²Area » Topic » SubtopicPosted by
Aharoni-Berger conjectureAharoni; Berger✭✭✭0Combinatorics » Matroid Theorymdevos
Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Theory » Graph Algorithmsfhavet
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Partial List ColoringAlbertson; Grossman; Haas✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0Topologyrybu
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
Splitting a digraph with minimum outdegree constraintsAlon✭✭✭0Graph Theory » Directed Graphsfhavet
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Graph Theory » Coloring » Vertex coloringfhavet
The Alon-Tarsi basis conjectureAlon; Linial; Meshulam✭✭0Combinatorics » Matricesmdevos
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Graph Theory » Directed Graphsfhavet
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Graph Theory » Basic G.T.mdevos
Even vs. odd latin squaresAlon; Tarsi✭✭✭0Combinatoricsmdevos
Rendezvous on a lineAlpern✭✭✭0Unsortedmdevos
Obstacle number of planar graphsAlpert; Koch; Laison✭1Graph TheoryAndrew King
Decomposing an even tournament in directed paths.Alspach; Mason; Pullman✭✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Chromatic number of random lifts of complete graphsAmit✭✭0Graph Theory » Probabilistic G.T.DOT
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0Topologyrybu
Fundamental group torsion for subsets of Euclidean 3-spaceAncient/folklore✭✭0Topologyrybu
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Graph Theory » Coloring » LabelingDOT
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Cycle Double Covers Containing Predefined 2-Regular SubgraphsArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
3-Edge-Coloring ConjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theoryarthur
Vertex Cover Integrality GapAtserias✭✭0Logic » Finite Model Theorydberwanger
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
Arc-disjoint strongly connected spanning subdigraphsBang-Jensen; Yeo✭✭0Graph Theoryfhavet
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Forcing a $K_6$-minorBarát ; Joret; Wood✭✭0Graph Theory » Basic G.T. » MinorsDavid Wood
Barnette's ConjectureBarnette✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Total Colouring ConjectureBehzad✭✭✭0Graph Theory » ColoringIradmusa
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
Beneš ConjectureBeneš✭✭✭0CombinatoricsVadim Lioubimov
Beneš Conjecture (graph-theoretic form)Beneš✭✭✭0Graph TheoryVadim Lioubimov
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Graph TheoryVadim Lioubimov
Shuffle-Exchange ConjectureBeneš; Folklore; Stone✭✭✭0CombinatoricsVadim Lioubimov
Approximation Ratio for Maximum Edge Disjoint Paths problemBentz✭✭0Graph Theoryjcmeyer
Approximation ratio for k-outerplanar graphsBentz✭✭0Graph Theoryjcmeyer
Finding k-edge-outerplanar graph embeddingsBentz✭✭0Graph Theoryjcmeyer
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Graph Theory » Directed GraphsJS
Distribution and upper bound of mimic numbersBhattacharyya✭✭1Number Theory » Analytic N.T.facility_cttb@i...
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Book Thickness of SubdivisionsBlankenship; Oporowski✭✭1Graph TheoryDavid Wood

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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