Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
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
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Simplexity of the n-cube✭✭✭1Geometrymdevos
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos
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
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Graph Theory » Algebraic G.T.mdevos
Inequality of the means✭✭✭0Geometrymdevos
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
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
Domination in cubic graphsReed✭✭0Graph Theory » Basic G.T.mdevos
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Theory » Graph Algorithmsmdevos
Friendly partitionsDeVos✭✭0Graph Theory » Basic G.T.mdevos
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Divisibility of central binomial coefficientsGraham✭✭1Number Theory » Combinatorial N.T.maxal
A sextic counterexample to Euler's sum of powers conjectureEuler✭✭1Number Theory » Computational N.T.maxal
Counterexamples to the Baillie-PSW primality test✭✭1Number Theory » Computational N.T.maxal
Diophantine quintuple conjecture✭✭1Number Theorymaxal
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Frobenius number of four or more integers✭✭1Number Theory » Combinatorial N.T.maxal
Special PrimesGeorge BALAN1Number Theorymaththebalans
Something like Picard for 1-formsElsner✭✭0AnalysisMathOMan
Sequence defined on multisetsErickson✭✭1CombinatoricsMartin Erickson
Square achievement game on an n x n gridErickson✭✭1CombinatoricsMartin Erickson
Exact colorings of graphsErickson✭✭0Graph TheoryMartin Erickson
Transversal achievement game on a square gridErickson✭✭1CombinatoricsMartin Erickson
Covering a square with unit squares✭✭0GeometryMartin Erickson
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Monochromatic vertex colorings inherited from Perfect Matchings✭✭✭1Graph TheoryMario Krenn
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
$C^r$ Stability ConjecturePalis; Smale✭✭✭✭0Analysism n
inverse of an integer matrixGregory✭✭0Algebralvoyster
Length of surreal productGonshor1CombinatoricsLukáš Lánský
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there infinite number of Mersenne Primes?✭✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
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