Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Graph Theory » Coloringmdevos
Coloring the union of degenerate graphsTarsi✭✭0Graph Theory » Coloringfhavet
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
Decomposing a connected graph into paths.Gallai✭✭✭0Graph Theory » Basic G.T. » Pathsfhavet
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Graph Theory » Basic G.T. » Pathsfhavet
Highly connected graphs with no K_n minorThomas✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Seagull problemSeymour✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Forcing a $K_6$-minorBarát ; Joret; Wood✭✭0Graph Theory » Basic G.T. » MinorsDavid Wood
Forcing a 2-regular minorReed; Wood✭✭1Graph Theory » Basic G.T. » MinorsDavid Wood
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Graph Theory » Basic G.T. » MatchingsJirka
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Cycle double cover conjectureSeymour; Szekeres✭✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
The circular embedding conjectureHaggard✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Faithful cycle coversSeymour✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Decomposing eulerian graphs✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Barnette's ConjectureBarnette✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Graph Theory » Basic G.T. » CyclesAgelos
Jones' conjectureKloks; Lee; Liu✭✭0Graph Theory » Basic G.T. » Cyclescmlee
Chords of longest cyclesThomassen✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Middle levels problemErdos✭✭0Graph Theory » Basic G.T. » Cyclestchow
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Graph Theory » Basic G.T. » Cyclestchow
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
Decomposing an eulerian graph into cycles.Hajós✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour.Sabidussi✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Partitioning edge-connectivityDeVos✭✭0Graph Theory » Basic G.T. » Connectivitymdevos
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
Graham's conjecture on tree reconstructionGraham✭✭0Graph Theory » Basic G.T.mdevos
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Graph Theory » Basic G.T.mdevos
Complete bipartite subgraphs of perfect graphsFox✭✭0Graph Theory » Basic G.T.mdevos
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Graph Theory » Basic G.T.andreasruedinger
Domination in cubic graphsReed✭✭0Graph Theory » Basic G.T.mdevos
Friendly partitionsDeVos✭✭0Graph Theory » Basic G.T.mdevos
Subgraph of large average degree and large girth.Thomassen✭✭0Graph Theory » Basic G.T.fhavet
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Graph Theory » Basic G.T.mhaythorpe
57-regular Moore graph?Hoffman; Singleton✭✭✭0Graph Theory » Algebraic G.T.mdevos
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Graph Theory » Algebraic G.T.mdevos
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
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