Graph Theory

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¿Are critical k-forests tight?Strausz✭✭0HypergraphsDino
Woodall's ConjectureWoodall✭✭✭0Directed Graphsmdevos
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Extremal G.T.boris
What is the largest graph of positive curvature?DeVos; Mohar1Topological G.T. » Planar graphsmdevos
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Coloring » Vertex coloringfhavet
Weak saturation of the cube in the cliqueMorrison; Noel1Extremal G.T.Jon Noel
Weak pentagon problemSamal✭✭0Coloring » HomomorphismsRobert Samal
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Iradmusa
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Coloring » Edge coloringmacajova
Universal point sets for planar graphsMohar✭✭✭0Topological G.T. » Drawingsmdevos
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Infinite Graphsmdevos
Unit vector flowsJain✭✭0Coloring » Nowhere-zero flowsmdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Infinite Graphsmdevos
Unfriendly partitionsCowan; Emerson✭✭✭0Infinite Graphsmdevos
Turán's problem for hypergraphsTuran✭✭0Hypergraphsfhavet
Turán number of a finite family.Erdos; Simonovits✭✭0fhavet
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Extremal G.T.fhavet
Triangle free strongly regular graphs✭✭✭0Algebraic G.T.mdevos
Total Colouring ConjectureBehzad✭✭✭0ColoringIradmusa
Three-chromatic (0,2)-graphsPayan✭✭0ColoringGordon Royle
The Two Color ConjectureNeumann-Lara✭✭0Directed Graphsmdevos
The three 4-flows conjectureDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Algorithmsmdevos
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Basic G.T. » Matchingsmdevos
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.mdevos
The Crossing Number of the HypercubeErdos; Guy✭✭0Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Graph✭✭✭0Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Topological G.T. » Crossing numbersRobert Samal
The circular embedding conjectureHaggard✭✭✭0Basic G.T. » Cyclesmdevos
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Andrew King
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Extremal G.T.asp
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Directed GraphsJS
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Basic G.T. » Matchingsmdevos
Switching reconstruction of digraphsBondy; Mercier✭✭0fhavet
Switching reconstruction conjectureStanley✭✭0fhavet
Subgraph of large average degree and large girth.Thomassen✭✭0Basic G.T.fhavet
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Directed Graphsfhavet
Strong matchings and coversAharoni✭✭✭0Infinite Graphsmdevos
Strong edge colouring conjectureErdos; Nesetril✭✭0Coloring » Edge coloringfhavet
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Coloring » Vertex coloringberger
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Basic G.T. » Cyclesarthur
Star chromatic index of cubic graphsDvorak; Mohar; Samal✭✭0Robert Samal
Star chromatic index of complete graphsDvorak; Mohar; Samal✭✭1Robert Samal
Stable set meeting all longest directed paths.Laborde; Payan; Xuong N.H.✭✭0fhavet
Splitting a digraph with minimum outdegree constraintsAlon✭✭✭0Directed Graphsfhavet
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Hypergraphsfhavet
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0mdevos
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Vadim Lioubimov
Shannon capacity of the seven-cycle✭✭✭0tchow
Seymour's self-minor conjectureSeymour✭✭✭0Infinite Graphsmdevos
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