Open Problems


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Sets with distinct subset sumsErdos✭✭✭0Number Theory » Combinatorial N.T.mdevos
Sequence defined on multisetsErickson✭✭1CombinatoricsMartin Erickson
Separators in string graphsFox; Pach; Tóth✭✭0Graph Theorycibulka
Seagull problemSeymour✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Saturation in the HypercubeMorrison; Noel; Scott✭✭0CombinatoricsJon Noel
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Ryser's conjectureRyser✭✭✭0Graph Theory » Hypergraphsmdevos
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
Rota's basis conjectureRota✭✭✭0Combinatorics » Matricesmdevos
Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
Rendezvous on a lineAlpern✭✭✭0Unsortedmdevos
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
Reed's omega, delta, and chi conjectureReed✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
Realisation problem for the space of knots in the 3-sphereBudney✭✭0Topologyrybu
Real roots of the flow polynomialWelsh✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Theory » Graph Algorithmsfhavet
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
Point sets with no empty pentagonWood1GeometryDavid Wood
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Pebbling a cartesian productGraham✭✭✭0Graph Theorymdevos
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
Partitioning edge-connectivityDeVos✭✭0Graph Theory » Basic G.T. » Connectivitymdevos
Partition of Complete Geometric Graph into Plane Trees✭✭0GeometryDavid Wood
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Graph Theory » Basic G.T. » Pathsfhavet
Partial List ColoringAlbertson; Grossman; Haas✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Partial List ColoringIradmusa✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Packing T-joinsDeVos✭✭0Graph Theory » Coloring » Edge coloringmdevos
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner
P vs. NPCook; Levin✭✭✭✭0Theoretical Comp. Sci. » Algorithmszitterbewegung
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
Outward reloid of composition vs composition of outward reloidsPorton✭✭0Topologyporton
Outer reloid of restricted funcoidPorton✭✭0Topologyporton
Oriented trees in n-chromatic digraphsBurr✭✭✭0Graph Theory » Directed Graphsfhavet
Oriented chromatic number of planar graphs✭✭0Graph Theory » Coloring » Vertex coloringRobert Samal
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
One-way functions exist✭✭✭✭0Theoretical Comp. Sci. » Complexityporton
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