Graph Theory

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Separators in string graphsFox; Pach; Tóth✭✭0cibulka
Frankl's union-closed sets conjectureFrankl✭✭0Hypergraphstchow
Do any three longest paths in a connected graph have a vertex in common? Gallai✭✭0fhavet
Decomposing a connected graph into paths.Gallai✭✭✭0Basic G.T. » Pathsfhavet
Are vertex minor closed classes chi-bounded?Geelen✭✭0Coloring » Vertex coloringmdevos
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Infinite GraphsRobert Samal
End-Devouring RaysGeorgakopoulos1Infinite GraphsAgelos
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Basic G.T. » CyclesAgelos
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Coloring » Vertex coloringmdevos
(2 + epsilon)-flow conjectureGoddyn; Seymour✭✭✭0Coloring » Nowhere-zero flowsmdevos
Goldberg's conjectureGoldberg✭✭✭0Coloring » Edge coloringmdevos
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Extremal G.T.boris
Graham's conjecture on tree reconstructionGraham✭✭0Basic G.T.mdevos
Pebbling a cartesian productGraham✭✭✭0mdevos
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Coloring » Edge coloringmacajova
Grunbaum's ConjectureGrunbaum✭✭✭0Topological G.T. » Coloringmdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Coloringmdevos
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Topological G.T.fhavet
Laplacian Degrees of a GraphGuo✭✭0Algebraic G.T.Robert Samal
Bounding the chromatic number of graphs with no odd holeGyarfas✭✭✭0Coloring » Vertex coloringmdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Coloring » Vertex coloringmdevos
The circular embedding conjectureHaggard✭✭✭0Basic G.T. » Cyclesmdevos
Decomposing an eulerian graph into cycles.Hajós✭✭0Basic G.T. » Cyclesfhavet
Edge Reconstruction ConjectureHarary✭✭✭0melch
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Directed Graphsfhavet
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1David Wood
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0David Wood
Erdös-Posa property for long directed cycles.Havet; Maia✭✭0Directed Graphsfhavet
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Basic G.T.mhaythorpe
Hedetniemi's ConjectureHedetniemi✭✭✭0Coloring » Vertex coloringmdevos
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Coloring » Vertex coloringJon Noel
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Directed Graphsfhavet
57-regular Moore graph?Hoffman; Singleton✭✭✭0Algebraic G.T.mdevos
Partial List ColoringIradmusa✭✭✭0Coloring » Vertex coloringIradmusa
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Iradmusa
Long directed cycles in diregular digraphsJackson✭✭✭0Directed Graphsfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Directed Graphsfhavet
Jaeger's modular orientation conjectureJaeger✭✭✭0Coloring » Nowhere-zero flowsmdevos
Petersen coloring conjectureJaeger✭✭✭0Coloring » Edge coloringmdevos
Mapping planar graphs to odd cyclesJaeger✭✭✭0Coloring » Homomorphismsmdevos
Unit vector flowsJain✭✭0Coloring » Nowhere-zero flowsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Basic G.T. » Minorsmdevos
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Basic G.T. » Cyclesfhavet
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Coloring » Vertex coloringDavid Wood
Reconstruction conjectureKelly; Ulam✭✭✭✭0zitterbewegung
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Basic G.T. » Pathsfhavet
Jones' conjectureKloks; Lee; Liu✭✭0Basic G.T. » Cyclescmlee
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Coloring » Vertex coloringAndrew King
Imbalance conjectureKozerenko✭✭0Sergiy Kozerenko
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