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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » Subtopicsort iconPosted by
Choice number of complete multipartite graphs with parts of size 4✭1Coloring » Vertex coloringjnoel12
On-Line Ohba's ConjectureHuang; Wong; Zhu✭✭1Coloring » Vertex coloringjnoel12
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Coloring » Vertex coloringjnoel12
Reconfiguration problems for graph colouringsNoel✭1Coloring » Vertex coloringjnoel12
5-flow conjectureTutte✭✭✭✭0Coloring » Nowhere-zero flowsmdevos
4-flow conjectureTutte✭✭✭0Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭0Coloring » Nowhere-zero flowsmdevos
(2 + epsilon)-flow conjectureGoddyn; Seymour✭✭✭0Coloring » Nowhere-zero flowsmdevos
Jaeger's modular orientation conjectureJaeger✭✭✭0Coloring » Nowhere-zero flowsmdevos
Bouchet's 6-flow conjectureBouchet✭✭✭0Coloring » Nowhere-zero flowsmdevos
The three 4-flows conjectureDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
A homomorphism problem for flowsDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
Real roots of the flow polynomialWelsh✭✭0Coloring » Nowhere-zero flowsmdevos
Unit vector flowsJain✭✭0Coloring » Nowhere-zero flowsmdevos
Antichains in the cycle continuous orderDeVos✭✭0Coloring » Nowhere-zero flowsmdevos
Graceful Tree Conjecture✭✭✭0Coloring » Labelingkintali
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Coloring » LabelingDOT
Cores of Cayley graphsSamal✭✭0Coloring » HomomorphismsRobert Samal
Pentagon problemNesetril✭✭✭0Coloring » HomomorphismsRobert Samal
Mapping planar graphs to odd cyclesJaeger✭✭✭0Coloring » Homomorphismsmdevos
Weak pentagon problemSamal✭✭0Coloring » HomomorphismsRobert Samal
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Coloring » Homomorphismsjfoniok
Circular choosability of planar graphsMohar✭0Coloring » Homomorphismsrosskang
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
Edge list coloring conjecture✭✭✭0Coloring » Edge coloringtchow
Seymour's r-graph conjectureSeymour✭✭✭0Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Coloring » Edge coloringmdevos
Strong edge colouring conjectureErdos; Nesetril✭✭0Coloring » Edge coloringfhavet
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
Linial-Berge path partition dualityBerge; Linial✭✭✭0Basic G.T. » Pathsberger
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
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
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
Cycle double cover conjectureSeymour; Szekeres✭✭✭✭0Basic G.T. » Cyclesmdevos
The circular embedding conjectureHaggard✭✭✭0Basic G.T. » Cyclesmdevos

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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