Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Are vertex minor closed classes chi-bounded?Geelen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Mixing Circular ColouringsBrewster; Noel1Graph Theory » Coloring » Vertex coloringJon Noel
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Melnikov's valency-variety problemMelnikov0Graph Theory » Coloring » Vertex coloringasp
Earth-Moon ProblemRingel✭✭1Graph Theory » Coloring » Vertex coloringfhavet
Acyclic list colouring of planar graphs.Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena✭✭✭0Graph Theory » Coloring » Vertex coloringfhavet
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Colouring the square of a planar graphWegner✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Choosability of Graph PowersNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Nonrepetitive colourings of planar graphsAlon N.; Grytczuk J.; Hałuszczak M.; Riordan O.✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
5-flow conjectureTutte✭✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
4-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Jaeger's modular orientation conjectureJaeger✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Bouchet's 6-flow conjectureBouchet✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The three 4-flows conjectureDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
A homomorphism problem for flowsDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Real roots of the flow polynomialWelsh✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Unit vector flowsJain✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Antichains in the cycle continuous orderDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Circular flow number of regular class 1 graphsSteffen✭✭0Graph Theory » Coloring » Nowhere-zero flowsEckhard Steffen
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Graph Theory » Coloring » LabelingDOT
Cores of Cayley graphsSamal✭✭✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Pentagon problemNesetril✭✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Weak pentagon problemSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Graph Theory » Coloring » Homomorphismsjfoniok
Circular choosability of planar graphsMohar0Graph Theory » Coloring » Homomorphismsrosskang
Petersen coloring conjectureJaeger✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Packing T-joinsDeVos✭✭0Graph Theory » Coloring » Edge coloringmdevos
Acyclic edge-colouringFiamcik✭✭0Graph Theory » Coloring » Edge coloringmdevos
A generalization of Vizing's Theorem?Rosenfeld✭✭0Graph Theory » Coloring » Edge coloringmdevos
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Graph Theory » Coloring » Edge coloringmacajova
Edge list coloring conjecture✭✭✭0Graph Theory » Coloring » Edge coloringtchow
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Strong edge colouring conjectureErdos; Nesetril✭✭0Graph Theory » Coloring » Edge coloringfhavet
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