Open Problems

TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
Complete bipartite subgraphs of perfect graphsFox✭✭0Graph Theory » Basic G.T.mdevos
Coloring random subgraphsBukh✭✭0Graph Theory » Probabilistic G.T.mdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Graph Theory » Coloringmdevos
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Jacobian ConjectureKeller✭✭✭0Geometry » Algebraic GeometryCharles
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Tarski's exponential function problemTarski✭✭0LogicCharles
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Edge-antipodal colorings of cubesNorine✭✭0Combinatorics » Ramsey Theorymdevos
Termination of the sixth Goodstein SequenceGraham0Logicmdevos
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
trace inequality✭✭0AlgebraMiwa Lin
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
Invariant subspace problem✭✭✭0Analysistchow
Shannon capacity of the seven-cycle✭✭✭0Graph Theorytchow
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Graph Theory » Algebraic G.T.mdevos
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
Sums of independent random variables with unbounded varianceFeige✭✭0Theoretical Comp. Sci.cwenner
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner
Inequality of the means✭✭✭0Geometrymdevos
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Graph Theory » Basic G.T.andreasruedinger
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Are vertex minor closed classes chi-bounded?Geelen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Domination in cubic graphsReed✭✭0Graph Theory » Basic G.T.mdevos
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
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