Open Problems


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A diagram about funcoids and reloidsPorton✭✭0Topologyporton
Which outer reloids are equal to inner onesPorton✭✭0Topologyporton
Waring rank of determinantTeitler✭✭0AlgebraZach Teitler
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
Edge-Unfolding Convex PolyhedraShephard✭✭0GeometryErik Demaine
4-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Bouchet's 6-flow conjectureBouchet✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The circular embedding conjectureHaggard✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Faithful cycle coversSeymour✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Decomposing eulerian graphs✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
A nowhere-zero point in a linear mappingJaeger✭✭✭0Combinatorics » Matricesmdevos
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
57-regular Moore graph?Hoffman; Singleton✭✭✭0Graph Theory » Algebraic G.T.mdevos
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Graph Theory » Algebraic G.T.mdevos
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
Subset-sums equality (pigeonhole version)✭✭✭0Theoretical Comp. Sci. » Complexitymdevos
Ryser's conjectureRyser✭✭✭0Graph Theory » Hypergraphsmdevos
Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Graph Theory » Coloring » Vertex coloringberger
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Woodall's ConjectureWoodall✭✭✭0Graph Theory » Directed Graphsmdevos
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
Fat 4-polytopesEppstein; Kuperberg; Ziegler✭✭✭0Geometry » Polytopesmdevos
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Reed's omega, delta, and chi conjectureReed✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
Bases of many weightsSchrijver; Seymour✭✭✭0Combinatorics » Matroid Theorymdevos
Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
Aharoni-Berger conjectureAharoni; Berger✭✭✭0Combinatorics » Matroid Theorymdevos
Barnette's ConjectureBarnette✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Sets with distinct subset sumsErdos✭✭✭0Number Theory » Combinatorial N.T.mdevos
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
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