Graph Theory

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Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0David Wood
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1David Wood
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Directed Graphsfhavet
Edge Reconstruction ConjectureHarary✭✭✭0melch
Decomposing an eulerian graph into cycles.Hajós✭✭0Basic G.T. » Cyclesfhavet
The circular embedding conjectureHaggard✭✭✭0Basic G.T. » Cyclesmdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Coloring » Vertex coloringmdevos
Laplacian Degrees of a GraphGuo✭✭0Algebraic G.T.Robert Samal
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Topological G.T.fhavet
Grunbaum's ConjectureGrunbaum✭✭✭0Topological G.T. » Coloringmdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Coloringmdevos
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Coloring » Edge coloringmacajova
Graham's conjecture on tree reconstructionGraham✭✭0Basic G.T.mdevos
Pebbling a cartesian productGraham✭✭✭0mdevos
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Extremal G.T.boris
Goldberg's conjectureGoldberg✭✭✭0Coloring » Edge coloringmdevos
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Coloring » Vertex coloringmdevos
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Basic G.T. » CyclesAgelos
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
Are vertex minor closed classes chi-bounded?Geelen✭✭0Coloring » Vertex coloringmdevos
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
Frankl's union-closed sets conjectureFrankl✭✭0Hypergraphstchow
Complete bipartite subgraphs of perfect graphsFox✭✭0Basic G.T.mdevos
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Coloring » Homomorphismsjfoniok
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Basic G.T. » Cyclesfhavet
Acyclic edge-colouringFiamcik✭✭0Coloring » Edge coloringmdevos
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Topological G.T. » ColoringDavid Wood
Exact colorings of graphsErickson✭✭0Martin Erickson
Turán number of a finite family.Erdos; Simonovits✭✭0fhavet
Strong edge colouring conjectureErdos; Nesetril✭✭0Coloring » Edge coloringfhavet
Double-critical graph conjectureErdos; Lovasz✭✭0Coloring » Vertex coloringDFR
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.mdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Infinite Graphsmdevos
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.Jon Noel
The Crossing Number of the HypercubeErdos; Guy✭✭0Topological G.T. » Crossing numbersRobert Samal
Odd-cycle transversal in triangle-free graphsErdos; Faudree; Pach; Spencer✭✭0Extremal G.T.fhavet
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Coloring » Vertex coloringJon Noel
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Robert Samal
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Robert Samal
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Infinite Graphsmdevos
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Topological G.T. » Crossing numbersmdevos
What is the largest graph of positive curvature?DeVos; Mohar1Topological G.T. » Planar graphsmdevos
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Coloring » Vertex coloringmdevos
The three 4-flows conjectureDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
A homomorphism problem for flowsDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
Packing T-joinsDeVos✭✭0Coloring » Edge coloringmdevos
Partitioning edge-connectivityDeVos✭✭0Basic G.T. » Connectivitymdevos
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