Open Problems

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Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)✭✭✭✭0TopologyJailton Viana
$C^r$ Stability ConjecturePalis; Smale✭✭✭✭0Analysism n
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0Number Theoryprinceps
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Graph Theory » Topological G.T. » ColoringDavid Wood
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
3-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
4-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Graph Theory » Coloringmdevos
5-flow conjectureTutte✭✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
5-local-tensionsDeVos✭✭0Graph Theory » Topological G.T. » Coloringmdevos
57-regular Moore graph?Hoffman; Singleton✭✭✭0Graph Theory » Algebraic G.T.mdevos
A conjecture about direct product of funcoidsPorton✭✭0Topologyporton
A conjecture on iterated circumcentresGoddyn✭✭1Geometrymdevos
A diagram about funcoids and reloidsPorton✭✭0Topologyporton
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
A funcoid related to directed topological spacesPorton✭✭0Topologyporton
A generalization of Vizing's Theorem?Rosenfeld✭✭0Graph Theory » Coloring » Edge coloringmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Theory » Graph Algorithmsmdevos
A homomorphism problem for flowsDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
A nowhere-zero point in a linear mappingJaeger✭✭✭0Combinatorics » Matricesmdevos
A sextic counterexample to Euler's sum of powers conjectureEuler✭✭1Number Theory » Computational N.T.maxal
Acyclic edge-colouringFiamcik✭✭0Graph Theory » Coloring » Edge coloringmdevos
Acyclic list colouring of planar graphs.Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena✭✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Ádám's ConjectureÁdám✭✭✭0Graph Theory » Directed Graphsfhavet
Aharoni-Berger conjectureAharoni; Berger✭✭✭0Combinatorics » Matroid Theorymdevos
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Graph Theory » Coloring » Homomorphismsjfoniok
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Graph Theory » Basic G.T.mhaythorpe
Another conjecture about reloids and funcoidsPorton✭✭0Topologyporton
Antichains in the cycle continuous orderDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Antidirected trees in digraphsAddario-Berry; Havet; Linhares Sales; Reed; Thomassé✭✭0Graph Theory » Directed Graphsfhavet
Approximation ratio for k-outerplanar graphsBentz✭✭0Graph Theoryjcmeyer
Approximation Ratio for Maximum Edge Disjoint Paths problemBentz✭✭0Graph Theoryjcmeyer
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Graph Theory » Directed Graphsfhavet
Arc-disjoint out-branching and in-branchingThomassen✭✭0Graph Theory » Directed Graphsfhavet
Arc-disjoint strongly connected spanning subdigraphsBang-Jensen; Yeo✭✭0Graph Theoryfhavet
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Are different notions of the crossing number the same?Pach; Tóth✭✭✭0Graph Theory » Topological G.T. » Crossing numberscibulka
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
Are there infinite number of Mersenne Primes?✭✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
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