Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Graph Theory » Extremal G.T.shudeshijie
Complexity of the H-factor problem.Kühn; Osthus✭✭0Graph Theory » Extremal G.T.fhavet
Odd-cycle transversal in triangle-free graphsErdos; Faudree; Pach; Spencer✭✭0Graph Theory » Extremal G.T.fhavet
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Graph Theory » Extremal G.T.fhavet
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
Weak saturation of the cube in the cliqueMorrison; Noel1Graph Theory » Extremal G.T.Jon Noel
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Theory » Graph Algorithmsmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Theory » Graph Algorithmsmdevos
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Theory » Graph Algorithmsfhavet
Ryser's conjectureRyser✭✭✭0Graph Theory » Hypergraphsmdevos
¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Frankl's union-closed sets conjectureFrankl✭✭0Graph Theory » Hypergraphstchow
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Graph Theory » Hypergraphsfhavet
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Graph Theory » Infinite Graphsmdevos
Unfriendly partitionsCowan; Emerson✭✭✭0Graph Theory » Infinite Graphsmdevos
Strong matchings and coversAharoni✭✭✭0Graph Theory » Infinite Graphsmdevos
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
End-Devouring RaysGeorgakopoulos1Graph Theory » Infinite GraphsAgelos
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos
Coloring random subgraphsBukh✭✭0Graph Theory » Probabilistic G.T.mdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Chromatic number of random lifts of complete graphsAmit✭✭0Graph Theory » Probabilistic G.T.DOT
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Large induced forest in a planar graph.Abertson; Berman✭✭0Graph Theory » Topological G.T.fhavet
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Graph Theory » Topological G.T.fhavet
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
5-local-tensionsDeVos✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Degenerate colorings of planar graphsBorodin✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
3-Colourability of Arrangements of Great CirclesFelsner; Hurtado; Noy; Streinu✭✭1Graph Theory » Topological G.T. » ColoringDavid Wood
The Crossing Number of the Complete Graph✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Crossing sequencesArchdeacon; Bonnington; Siran✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Are different notions of the crossing number the same?Pach; Tóth✭✭✭0Graph Theory » Topological G.T. » Crossing numberscibulka
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
What is the largest graph of positive curvature?DeVos; Mohar1Graph Theory » Topological G.T. » Planar graphsmdevos
Growth of finitely presented groupsAdyan✭✭✭0Group Theorymdevos
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