Open Problems


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Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Point sets with no empty pentagonWood1GeometryDavid Wood
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Theory » Graph Algorithmsfhavet
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
Question about 'solving' something✭✭0Algebratigris35711
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
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Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
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Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
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Real roots of the flow polynomialWelsh✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
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Realisation problem for the space of knots in the 3-sphereBudney✭✭0Topologyrybu
Reconstruction conjectureKelly; Ulam✭✭✭✭0Graph Theoryzitterbewegung
Reed's omega, delta, and chi conjectureReed✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
Rendezvous on a lineAlpern✭✭✭0Unsortedmdevos
Rendezvous on a line✭✭0Algebratigris35711
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Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
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Ryser's conjectureRyser✭✭✭0Graph Theory » Hypergraphsmdevos
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
Saturation in the HypercubeMorrison; Noel; Scott✭✭0CombinatoricsJon Noel
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
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