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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » SubtopicPosted bysort icon
The Crossing Number of the HypercubeErdos; Guy✭✭0Topological G.T. » Crossing numbersRobert Samal
Barnette's ConjectureBarnette✭✭✭0Basic G.T. » CyclesRobert Samal
List colorings of edge-critical graphsMohar✭✭0Coloring » Edge coloringRobert Samal
Laplacian Degrees of a GraphGuo✭✭0Algebraic G.T.Robert Samal
Weak pentagon problemSamal✭✭0Coloring » HomomorphismsRobert Samal
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Basic G.T. » CyclesRobert Samal
Infinite uniquely hamiltonian graphsMohar✭✭0Infinite GraphsRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Basic G.T. » CyclesRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Infinite GraphsRobert Samal
Oriented chromatic number of planar graphs✭✭0Coloring » Vertex coloringRobert Samal
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Topological G.T. » Crossing numbersRobert Samal
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Robert Samal
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Robert Samal
Circular choosability of planar graphsMohar✭0Coloring » Homomorphismsrosskang
Imbalance conjectureKozerenko✭✭0Sergiy Kozerenko
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Extremal G.T.shudeshijie
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Topological G.T. » Drawingstaxipom
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Basic G.T. » Cyclestchow
Frankl's union-closed sets conjectureFrankl✭✭0Hypergraphstchow
Edge list coloring conjecture✭✭✭0Coloring » Edge coloringtchow
Shannon capacity of the seven-cycle✭✭✭0tchow
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Vadim Lioubimov
Beneš Conjecture (graph-theoretic form)Beneš✭✭✭0Vadim Lioubimov
Matching cut and girth✭✭0w
Reconstruction conjectureKelly; Ulam✭✭✭✭0zitterbewegung

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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