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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » Subtopicsort iconPosted by
Pebbling a cartesian productGraham✭✭✭0mdevos
Reconstruction conjectureKelly; Ulam✭✭✭✭0zitterbewegung
Edge Reconstruction ConjectureHarary✭✭✭0melch
Book Thickness of SubdivisionsBlankenship; Oporowski✭✭1David Wood
Shannon capacity of the seven-cycle✭✭✭0tchow
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Andrew King
Number of Cliques in Minor-Closed ClassesWood✭✭0David Wood
Shuffle-Exchange Conjecture (graph-theoretic form)Beneš; Folklore; Stone✭✭✭0Vadim Lioubimov
Separators in string graphsFox; Pach; Tóth✭✭0cibulka
Odd cycles and low oddness✭✭0Gagik
57-regular Moore graph?Hoffman; Singleton✭✭✭0Algebraic G.T.mdevos
Hamiltonian paths and cycles in vertex transitive graphsLovasz✭✭✭0Algebraic G.T.mdevos
Fowler's Conjecture on eigenvalues of (3,6)-polyhedraFowler✭✭0Algebraic G.T.Robert Samal
Triangle free strongly regular graphs✭✭✭0Algebraic G.T.mdevos
Half-integral flow polynomial valuesMohar✭✭0Algebraic G.T.mohar
Ramsey properties of Cayley graphsAlon✭✭✭0Algebraic G.T.mdevos
Laplacian Degrees of a GraphGuo✭✭0Algebraic G.T.Robert Samal
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Algebraic G.T.mdevos
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Algebraic G.T.mdevos
Graham's conjecture on tree reconstructionGraham✭✭0Basic G.T.mdevos
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
Partitioning edge-connectivityDeVos✭✭0Basic G.T. » Connectivitymdevos
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
Uniquely hamiltonian graphsSheehan✭✭✭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
Bigger cycles in cubic graphs✭✭0Basic G.T. » Cyclesmdevos
Jones' conjectureKloks; Lee; Liu✭✭0Basic G.T. » Cyclescmlee
Chords of longest cyclesThomassen✭✭✭0Basic G.T. » Cyclesmdevos
Short cycle coversAlon; Tarsi✭✭0Basic G.T. » CyclesRobert Samal
Middle levels problemErdos✭✭0Basic G.T. » Cyclestchow
Hamiltonicity of Cayley graphsRapaport-Strasser✭✭✭1Basic G.T. » Cyclestchow
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
Exponentially many perfect matchings in cubic graphsLovasz; Plummer✭✭✭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
Linial-Berge path partition dualityBerge; Linial✭✭✭0Basic G.T. » Pathsberger

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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