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Open Problems


TitleAuthor(s)sort iconImp.¹Rec.²Area » Topic » SubtopicPosted by
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
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Few subsequence sums in Z_n x Z_nBollobas; Leader✭✭0Number Theory » Combinatorial N.T.mdevos
Cyclic spanning subdigraph with small cyclomatic numberBondy✭✭0Graph Theory » Directed Graphsfhavet
Switching reconstruction of digraphsBondy; Mercier✭✭0Graph Theoryfhavet
Degenerate colorings of planar graphsBorodin✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Acyclic list colouring of planar graphs.Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena✭✭✭0Graph Theory » Coloring » Vertex coloringfhavet
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Graph TheoryAndrew King
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
Bouchet's 6-flow conjectureBouchet✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Mixing Circular ColouringsBrewster; Noel✭1Graph Theory » Coloring » Vertex coloringJon Noel
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
Realisation problem for the space of knots in the 3-sphereBudney✭✭0Topologyrybu
Coloring random subgraphsBukh✭✭0Graph Theory » Probabilistic G.T.mdevos
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
Oriented trees in n-chromatic digraphsBurr✭✭✭0Graph Theory » Directed Graphsfhavet
Caccetta-Häggkvist ConjectureCaccetta; Häggkvist✭✭✭✭0Graph Theory » Directed Graphsfhavet
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Theory » Graph Algorithmsmdevos
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Graph Theory » Infinite Graphsmdevos
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Closing Lemma for Diffeomorphism (Dynamical Systems)Charles Pugh✭✭✭✭0TopologyJailton Viana
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Chowla's cosine problemChowla✭✭✭0Number Theorymdevos
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
P vs. NPCook; Levin✭✭✭✭0Theoretical Comp. Sci. » Algorithmszitterbewegung
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Unfriendly partitionsCowan; Emerson✭✭✭0Graph Theory » Infinite Graphsmdevos
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0Topologyporton
Dividing up the unrestricted partitionsDavid S.; Newman✭✭0CombinatoricsDavidSNewman
Monotone 4-term Arithmetic ProgressionsDavis; Entringer; Graham; Simmons✭✭0Combinatoricsvjungic
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
The three 4-flows conjectureDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
A homomorphism problem for flowsDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Packing T-joinsDeVos✭✭0Graph Theory » Coloring » Edge coloringmdevos
Partitioning edge-connectivityDeVos✭✭0Graph Theory » Basic G.T. » Connectivitymdevos
Antichains in the cycle continuous orderDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Gao's theorem for nonabelian groupsDeVos✭✭0Number Theory » Combinatorial N.T.mdevos
5-local-tensionsDeVos✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Friendly partitionsDeVos✭✭0Graph Theory » Basic G.T.mdevos
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos

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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