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Graph Theory


TitleAuthor(s)Imp.¹sort iconRec.²Topic » SubtopicPosted by
What is the largest graph of positive curvature?DeVos; Mohar✭1Topological G.T. » Planar graphsmdevos
End-Devouring RaysGeorgakopoulos✭1Infinite GraphsAgelos
Covering powers of cycles with equivalence subgraphs✭0Andrew King
Obstacle number of planar graphsAlpert; Koch; Laison✭1Andrew King
Circular choosability of planar graphsMohar✭0Coloring » Homomorphismsrosskang
Mixing Circular ColouringsBrewster; Noel✭1Coloring » Vertex coloringJon Noel
Melnikov's valency-variety problemMelnikov✭0Coloring » Vertex coloringasp
Weak saturation of the cube in the cliqueMorrison; Noel✭1Extremal G.T.Jon Noel
Cores of Cayley graphsSamal✭✭0Coloring » HomomorphismsRobert Samal
The three 4-flows conjectureDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
A homomorphism problem for flowsDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
Real roots of the flow polynomialWelsh✭✭0Coloring » Nowhere-zero flowsmdevos
Unit vector flowsJain✭✭0Coloring » Nowhere-zero flowsmdevos
Packing T-joinsDeVos✭✭0Coloring » Edge coloringmdevos
Acyclic edge-colouringFiamcik✭✭0Coloring » Edge coloringmdevos
Partitioning edge-connectivityDeVos✭✭0Basic G.T. » Connectivitymdevos
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Algorithmsmdevos
Graham's conjecture on tree reconstructionGraham✭✭0Basic G.T.mdevos
The Two Color ConjectureNeumann-Lara✭✭0Directed Graphsmdevos
A generalization of Vizing's Theorem?Rosenfeld✭✭0Coloring » Edge coloringmdevos
The Crossing Number of the HypercubeErdos; Guy✭✭0Topological G.T. » Crossing numbersRobert Samal
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Topological G.T. » Crossing numbersmdevos
Antichains in the cycle continuous orderDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
Half-integral flow polynomial valuesMohar✭✭0Algebraic G.T.mohar
List colorings of edge-critical graphsMohar✭✭0Coloring » Edge coloringRobert Samal
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Coloring » Vertex coloringmdevos
Laplacian Degrees of a GraphGuo✭✭0Algebraic G.T.Robert Samal
5-local-tensionsDeVos✭✭0Topological G.T. » Coloringmdevos
Weak pentagon problemSamal✭✭0Coloring » HomomorphismsRobert Samal
Infinite uniquely hamiltonian graphsMohar✭✭0Infinite GraphsRobert 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
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Basic G.T. » CyclesAgelos
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Basic G.T. » Matchingsmdevos
¿Are critical k-forests tight?Strausz✭✭0HypergraphsDino
Three-chromatic (0,2)-graphsPayan✭✭0ColoringGordon Royle
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Extremal G.T.boris
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Topological G.T. » Drawingstaxipom
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Basic G.T. » MatchingsJirka
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Directed GraphsJS
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Coloring » Edge coloringmacajova
Jones' conjectureKloks; Lee; Liu✭✭0Basic G.T. » Cyclescmlee
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Infinite Graphsmdevos
Random stable roommatesMertens✭✭0Basic G.T. » Matchingsmdevos
Complete bipartite subgraphs of perfect graphsFox✭✭0Basic G.T.mdevos
Coloring random subgraphsBukh✭✭0Probabilistic G.T.mdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Coloringmdevos
Negative association in uniform forestsPemantle✭✭0Probabilistic G.T.mdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Coloring » Vertex coloringmdevos

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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