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TitleAuthor(s)sort iconImp.¹Rec.²Area » Topic » SubtopicPosted by
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
Criterion for boundedness of power seriesRüdinger✭1Analysisandreasruedinger
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Graph Theory » Basic G.T.andreasruedinger
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Graph Theory » Basic G.T. » MatchingsJirka
Ryser's conjectureRyser✭✭✭0Graph Theory » Hypergraphsmdevos
Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour.Sabidussi✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Cores of Cayley graphsSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Weak pentagon problemSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphsfhavet
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Bases of many weightsSchrijver; Seymour✭✭✭0Combinatorics » Matroid Theorymdevos
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
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
Cycle double cover conjectureSeymour; Szekeres✭✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Edge-Unfolding Convex PolyhedraShephard✭✭0GeometryErik Demaine
Sidorenko's ConjectureSidorenko✭✭✭0Graph TheoryJon Noel
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Graph Theory » Algebraic G.T.mdevos
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Circular flow number of regular class 1 graphsSteffen✭✭0Graph Theory » Coloring » Nowhere-zero flowsEckhard Steffen
Circular flow numbers of $r$-graphsSteffen✭✭0Graph TheoryEckhard Steffen
¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Coloring the union of degenerate graphsTarsi✭✭0Graph Theory » Coloringfhavet
Tarski's exponential function problemTarski✭✭0LogicCharles
Waring rank of determinantTeitler✭✭0AlgebraZach Teitler
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Directed path of length twice the minimum outdegreeThomassé✭✭✭0Graph Theory » Directed Graphsfhavet
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
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
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

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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