Open Problems


TitleAuthor(s)sort iconImp.¹Rec.²Area » Topic » SubtopicPosted by
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Graph Theory » Extremal G.T.shudeshijie
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0Graph Theoryfhavet
Woodall's ConjectureWoodall✭✭✭0Graph Theory » Directed Graphsmdevos
Number of Cliques in Minor-Closed ClassesWood✭✭0Graph TheoryDavid Wood
Point sets with no empty pentagonWood1GeometryDavid Wood
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
Real roots of the flow polynomialWelsh✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Colouring the square of a planar graphWegner✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Graph Theory » Extremal G.T.fhavet
5-flow conjectureTutte✭✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
4-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Hamiltonian cycles in line graphsThomassen✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Chords of longest cyclesThomassen✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Arc-disjoint out-branching and in-branchingThomassen✭✭0Graph Theory » Directed Graphsfhavet
Subgraph of large average degree and large girth.Thomassen✭✭0Graph Theory » Basic G.T.fhavet
Edge-disjoint Hamilton cycles in highly strongly connected tournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Directed path of length twice the minimum outdegreeThomassé✭✭✭0Graph Theory » Directed Graphsfhavet
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Waring rank of determinantTeitler✭✭0AlgebraZach Teitler
Tarski's exponential function problemTarski✭✭0LogicCharles
Coloring the union of degenerate graphsTarsi✭✭0Graph Theory » Coloringfhavet
¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Circular flow number of regular class 1 graphsSteffen✭✭0Graph Theory » Coloring » Nowhere-zero flowsEckhard Steffen
Circular flow numbers of $r$-graphsSteffen✭✭0Graph TheoryEckhard Steffen
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Graph Theory » Algebraic G.T.mdevos
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
Edge-Unfolding Convex PolyhedraShephard✭✭0GeometryErik Demaine
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Cycle double cover conjectureSeymour; Szekeres✭✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Faithful cycle coversSeymour✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
Seagull problemSeymour✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
Bases of many weightsSchrijver; Seymour✭✭✭0Combinatorics » Matroid Theorymdevos
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
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