Open Problems


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Acyclic list colouring of planar graphs.Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena✭✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphsfhavet
Cycle Double Covers Containing Predefined 2-Regular SubgraphsArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Monochromatic vertex colorings inherited from Perfect Matchings✭✭✭1Graph TheoryMario Krenn
The three 4-flows conjectureDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
A homomorphism problem for flowsDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Real roots of the flow polynomialWelsh✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Unit vector flowsJain✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Packing T-joinsDeVos✭✭0Graph Theory » Coloring » Edge coloringmdevos
Acyclic edge-colouringFiamcik✭✭0Graph Theory » Coloring » Edge coloringmdevos
Partitioning edge-connectivityDeVos✭✭0Graph Theory » Basic G.T. » Connectivitymdevos
The permanent conjectureKahn✭✭0Combinatorics » Matricesmdevos
The Alon-Tarsi basis conjectureAlon; Linial; Meshulam✭✭0Combinatorics » Matricesmdevos
Olson's ConjectureOlson✭✭0Number Theory » Combinatorial N.T.mdevos
Few subsequence sums in Z_n x Z_nBollobas; Leader✭✭0Number Theory » Combinatorial N.T.mdevos
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Theory » Graph Algorithmsmdevos
Graham's conjecture on tree reconstructionGraham✭✭0Graph Theory » Basic G.T.mdevos
The Two Color ConjectureNeumann-Lara✭✭0Graph Theory » Directed Graphsmdevos
A generalization of Vizing's Theorem?Rosenfeld✭✭0Graph Theory » Coloring » Edge coloringmdevos
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Antichains in the cycle continuous orderDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Gao's theorem for nonabelian groupsDeVos✭✭0Number Theory » Combinatorial N.T.mdevos
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
A conjecture on iterated circumcentresGoddyn✭✭1Geometrymdevos
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
5-local-tensionsDeVos✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
Weak pentagon problemSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Complexity of square-root sumGoemans✭✭0Theoretical Comp. Sci. » Complexityabie
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Covering systems with big moduliErdos; Selfridge✭✭0Number Theory » Combinatorial N.T.Robert Samal
Oriented chromatic number of planar graphs✭✭0Graph Theory » Coloring » Vertex coloringRobert Samal
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