Also see: Graph Theory » Topological G.T. » Coloring
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Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Vertex coloringfhavet
Weak pentagon problemSamal✭✭0HomomorphismsRobert Samal
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Edge coloringmacajova
Unit vector flowsJain✭✭0Nowhere-zero flowsmdevos
Total Colouring ConjectureBehzad✭✭✭0Iradmusa
Three-chromatic (0,2)-graphsPayan✭✭0Gordon Royle
The three 4-flows conjectureDeVos✭✭0Nowhere-zero flowsmdevos
Strong edge colouring conjectureErdos; Nesetril✭✭0Edge coloringfhavet
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Vertex coloringberger
Seymour's r-graph conjectureSeymour✭✭✭0Edge coloringmdevos
Reed's omega, delta, and chi conjectureReed✭✭✭0Vertex coloringmdevos
Real roots of the flow polynomialWelsh✭✭0Nowhere-zero flowsmdevos
Petersen coloring conjectureJaeger✭✭✭0Edge coloringmdevos
Pentagon problemNesetril✭✭✭0HomomorphismsRobert Samal
Partial List ColoringAlbertson; Grossman; Haas✭✭✭0Vertex coloringIradmusa
Partial List ColoringIradmusa✭✭✭0Vertex coloringIradmusa
Packing T-joinsDeVos✭✭0Edge coloringmdevos
Oriented chromatic number of planar graphs✭✭0Vertex coloringRobert Samal
Mixing Circular ColouringsBrewster; Noel1Vertex coloringJon Noel
Melnikov's valency-variety problemMelnikov0Vertex coloringasp
Mapping planar graphs to odd cyclesJaeger✭✭✭0Homomorphismsmdevos
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Jon Noel
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Vertex coloringDavid Wood
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Vertex coloringJon Noel
List colorings of edge-critical graphsMohar✭✭0Edge coloringRobert Samal
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Vertex coloringfhavet
Linial-Berge path partition dualityBerge; Linial✭✭✭0berger
Jaeger's modular orientation conjectureJaeger✭✭✭0Nowhere-zero flowsmdevos
Hedetniemi's ConjectureHedetniemi✭✭✭0Vertex coloringmdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Vertex coloringmdevos
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0LabelingDOT
Goldberg's conjectureGoldberg✭✭✭0Edge coloringmdevos
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Vertex coloringJon Noel
Edge list coloring conjecture✭✭✭0Edge coloringtchow
Earth-Moon ProblemRingel✭✭1Vertex coloringfhavet
Double-critical graph conjectureErdos; Lovasz✭✭0Vertex coloringDFR
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Vertex coloringJon Noel
Counting 3-colorings of the hex latticeThomassen✭✭0Vertex coloringmdevos
Cores of Cayley graphsSamal✭✭0HomomorphismsRobert Samal
Colouring the square of a planar graphWegner✭✭0Vertex coloringfhavet
Coloring the union of degenerate graphsTarsi✭✭0fhavet
Coloring the Odd Distance GraphRosenfeld✭✭✭0Vertex coloringmdevos
Coloring and immersionAbu-Khzam; Langston✭✭✭1Vertex coloringmdevos
Circular flow number of regular class 1 graphsSteffen✭✭0Nowhere-zero flowsEckhard Steffen
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Vertex coloringmdevos
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Vertex coloringmdevos
Circular choosability of planar graphsMohar0Homomorphismsrosskang
Choosability of Graph PowersNoel✭✭1Vertex coloringJon Noel
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Vertex coloringJon Noel
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Vertex coloringJon Noel
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