Open Problems


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List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Big Line or Big Clique in Planar Point SetsKara; Por; Wood✭✭1GeometryDavid Wood
Cube-Simplex conjectureKalai✭✭✭0Geometry » Polytopesmdevos
The Double Cap ConjectureKalai✭✭0CombinatoricsJon Noel
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
The permanent conjectureKahn✭✭0Combinatorics » Matricesmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Unit vector flowsJain✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
A nowhere-zero point in a linear mappingJaeger✭✭✭0Combinatorics » Matricesmdevos
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Long directed cycles in diregular digraphsJackson✭✭✭0Graph Theory » Directed Graphsfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Graph Theory » Directed Graphsfhavet
Partial List ColoringIradmusa✭✭✭0Graph Theory » Coloring » Vertex coloringIradmusa
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Graph TheoryIradmusa
Edge-Colouring Geometric Complete GraphsHurtado✭✭1GeometryDavid Wood
57-regular Moore graph?Hoffman; Singleton✭✭✭0Graph Theory » Algebraic G.T.mdevos
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Hedetniemi's ConjectureHedetniemi✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Graph Theory » Basic G.T.mhaythorpe
Erdős-Posa property for long directed cyclesHavet; Maia✭✭0Graph Theory » Directed Graphsfhavet
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0Graph TheoryDavid Wood
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1Graph TheoryDavid Wood
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Graph Theory » Directed Graphsfhavet
Edge Reconstruction ConjectureHarary✭✭✭0Graph Theorymelch
Decomposing an eulerian graph into cycles.Hajós✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
The circular embedding conjectureHaggard✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Graph Theory » Topological G.T.fhavet
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Graph Theory » Coloringmdevos
inverse of an integer matrixGregory✭✭0Algebralvoyster
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
MSO alternation hierarchy over picturesGrandjean✭✭0Logic » Finite Model Theorydberwanger
Graham's conjecture on tree reconstructionGraham✭✭0Graph Theory » Basic G.T.mdevos
Divisibility of central binomial coefficientsGraham✭✭1Number Theory » Combinatorial N.T.maxal
Pebbling a cartesian productGraham✭✭✭0Graph Theorymdevos
Termination of the sixth Goodstein SequenceGraham0Logicmdevos
General position subsetsGowers✭✭0GeometryDavid Wood
Combinatorial covering designsGordon; Mills; Rödl; Schönheim0Combinatorics » DesignsPseudonym
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
Length of surreal productGonshor1CombinatoricsLukáš Lánský
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
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