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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » SubtopicPosted bysort icon
Packing T-joinsDeVos✭✭0Coloring » Edge coloringmdevos
Acyclic edge-colouringFiamcik✭✭0Coloring » Edge coloringmdevos
Partitioning edge-connectivityDeVos✭✭0Basic G.T. » Connectivitymdevos
Highly connected graphs with no K_n minorThomas✭✭✭0Basic G.T. » Minorsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Basic G.T. » Minorsmdevos
What is the largest graph of positive curvature?DeVos; Mohar✭1Topological G.T. » Planar graphsmdevos
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Algorithmsmdevos
57-regular Moore graph?Hoffman; Singleton✭✭✭0Algebraic G.T.mdevos
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Algebraic G.T.mdevos
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.mdevos
Graham's conjecture on tree reconstructionGraham✭✭0Basic G.T.mdevos
Ryser's conjectureRyser✭✭✭0Hypergraphsmdevos
The Two Color ConjectureNeumann-Lara✭✭0Directed Graphsmdevos
Grunbaum's ConjectureGrunbaum✭✭✭0Topological G.T. » Coloringmdevos
Woodall's ConjectureWoodall✭✭✭0Directed Graphsmdevos
A generalization of Vizing's Theorem?Rosenfeld✭✭0Coloring » Edge coloringmdevos
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Topological G.T. » Crossing numbersmdevos
Antichains in the cycle continuous orderDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
Universal point sets for planar graphsMohar✭✭✭0Topological G.T. » Drawingsmdevos
Seymour's self-minor conjectureSeymour✭✭✭0Infinite Graphsmdevos
Reed's omega, delta, and chi conjectureReed✭✭✭0Coloring » Vertex coloringmdevos
Triangle free strongly regular graphs✭✭✭0Algebraic G.T.mdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Infinite Graphsmdevos
Ramsey properties of Cayley graphsAlon✭✭✭0Algebraic G.T.mdevos
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Coloring » Vertex coloringmdevos
5-local-tensionsDeVos✭✭0Topological G.T. » Coloringmdevos
Mapping planar graphs to odd cyclesJaeger✭✭✭0Coloring » Homomorphismsmdevos
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Basic G.T. » Matchingsmdevos
Coloring and immersionAbu-Khzam; Langston✭✭✭1Coloring » Vertex coloringmdevos
Pebbling a cartesian productGraham✭✭✭0mdevos
Coloring the Odd Distance GraphRosenfeld✭✭✭0Coloring » Vertex coloringmdevos
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Infinite Graphsmdevos
Unfriendly partitionsCowan; Emerson✭✭✭0Infinite Graphsmdevos
Strong matchings and coversAharoni✭✭✭0Infinite Graphsmdevos
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Infinite Graphsmdevos
Chords of longest cyclesThomassen✭✭✭0Basic G.T. » Cyclesmdevos
Seagull problemSeymour✭✭✭0Basic G.T. » Minorsmdevos
Random stable roommatesMertens✭✭0Basic G.T. » Matchingsmdevos
Degenerate colorings of planar graphsBorodin✭✭✭0Topological G.T. » Coloringmdevos
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Basic G.T.mdevos
Hedetniemi's ConjectureHedetniemi✭✭✭0Coloring » Vertex coloringmdevos
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Algebraic G.T.mdevos
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
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Infinite Graphsmdevos
Negative association in uniform forestsPemantle✭✭0Probabilistic G.T.mdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Coloring » Vertex coloringmdevos
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Directed Graphsmdevos
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Directed Graphs » Tournamentsmdevos

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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