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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » Subtopicsort iconPosted by
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Basic G.T.mdevos
Complete bipartite subgraphs of perfect graphsFox✭✭0Basic G.T.mdevos
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Basic G.T.andreasruedinger
Domination in cubic graphsReed✭✭0Basic G.T.mdevos
Friendly partitionsDeVos✭✭0Basic G.T.mdevos
Subgraph of large average degree and large girth.Thomassen✭✭0Basic G.T.fhavet
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Basic G.T.mhaythorpe
Partitioning edge-connectivityDeVos✭✭0Basic G.T. » Connectivitymdevos
Kriesell's ConjectureKriesell✭✭0Basic G.T. » ConnectivityJon Noel
Cycle double cover conjectureSeymour; Szekeres✭✭✭✭0Basic G.T. » Cyclesmdevos
The circular embedding conjectureHaggard✭✭✭0Basic G.T. » Cyclesmdevos
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Basic G.T. » Cyclesmdevos
Faithful cycle coversSeymour✭✭✭0Basic G.T. » Cyclesmdevos
Decomposing eulerian graphs✭✭✭0Basic G.T. » Cyclesmdevos
Barnette's ConjectureBarnette✭✭✭0Basic G.T. » CyclesRobert Samal
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Basic G.T. » CyclesRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Basic G.T. » CyclesRobert Samal
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Basic G.T. » CyclesAgelos
Jones' conjectureKloks; Lee; Liu✭✭0Basic G.T. » Cyclescmlee
Chords of longest cyclesThomassen✭✭✭0Basic G.T. » Cyclesmdevos
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Basic G.T. » Cyclestchow
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Basic G.T. » Cyclesarthur
Decomposing an eulerian graph into cycles.Hajós✭✭0Basic G.T. » Cyclesfhavet
Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour.Sabidussi✭✭0Basic G.T. » Cyclesfhavet
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Basic G.T. » Cyclesfhavet
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Basic G.T. » Cyclesfhavet
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Basic G.T. » Cyclesfhavet
The Berge-Fulkerson conjectureBerge; Fulkerson✭✭✭✭0Basic G.T. » Matchingsmdevos
The intersection of two perfect matchingsMacajova; Skoviera✭✭0Basic G.T. » Matchingsmdevos
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Basic G.T. » MatchingsJirka
Random stable roommatesMertens✭✭0Basic G.T. » Matchingsmdevos
Highly connected graphs with no K_n minorThomas✭✭✭0Basic G.T. » Minorsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Basic G.T. » Minorsmdevos
Seagull problemSeymour✭✭✭0Basic G.T. » Minorsmdevos
Forcing a $K_6$-minorBarát ; Joret; Wood✭✭0Basic G.T. » MinorsDavid Wood
Forcing a 2-regular minorReed; Wood✭✭1Basic G.T. » MinorsDavid Wood
Decomposing a connected graph into paths.Gallai✭✭✭0Basic G.T. » Pathsfhavet
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Basic G.T. » Pathsfhavet
Linial-Berge path partition dualityBerge; Linial✭✭✭0Coloringberger
Three-chromatic (0,2)-graphsPayan✭✭0ColoringGordon Royle
Total Colouring ConjectureBehzad✭✭✭0ColoringIradmusa
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Coloringmdevos
Coloring the union of degenerate graphsTarsi✭✭0Coloringfhavet
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0ColoringJon Noel
Petersen coloring conjectureJaeger✭✭✭0Coloring » Edge coloringmdevos
Packing T-joinsDeVos✭✭0Coloring » Edge coloringmdevos
Acyclic edge-colouringFiamcik✭✭0Coloring » Edge coloringmdevos
A generalization of Vizing's Theorem?Rosenfeld✭✭0Coloring » Edge coloringmdevos
List colorings of edge-critical graphsMohar✭✭0Coloring » Edge coloringRobert Samal
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Coloring » Edge coloringmacajova

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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