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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » Subtopicsort iconPosted by
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
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
Graceful Tree Conjecture✭✭✭0Coloring » Labelingkintali
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Coloring » LabelingDOT
5-flow conjectureTutte✭✭✭✭0Coloring » Nowhere-zero flowsmdevos
4-flow conjectureTutte✭✭✭0Coloring » Nowhere-zero flowsmdevos
3-flow conjectureTutte✭✭✭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
Circular flow number of regular class 1 graphsSteffen✭✭0Coloring » Nowhere-zero flowsEckhard Steffen
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Coloring » Vertex coloringberger
Reed's omega, delta, and chi conjectureReed✭✭✭0Coloring » Vertex coloringmdevos
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Coloring » Vertex coloringmdevos
Oriented chromatic number of planar graphs✭✭0Coloring » Vertex coloringRobert Samal
Coloring and immersionAbu-Khzam; Langston✭✭✭1Coloring » Vertex coloringmdevos
Coloring the Odd Distance GraphRosenfeld✭✭✭0Coloring » Vertex coloringmdevos
Partial List ColoringAlbertson; Grossman; Haas✭✭✭0Coloring » Vertex coloringIradmusa
Partial List ColoringIradmusa✭✭✭0Coloring » Vertex coloringIradmusa
Hedetniemi's ConjectureHedetniemi✭✭✭0Coloring » Vertex coloringmdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Coloring » Vertex coloringmdevos
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Coloring » Vertex coloringmdevos
Double-critical graph conjectureErdos; Lovasz✭✭0Coloring » Vertex coloringDFR
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Coloring » Vertex coloringAndrew King
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Coloring » Vertex coloringmdevos
Are vertex minor closed classes chi-bounded?Geelen✭✭0Coloring » Vertex coloringmdevos
Mixing Circular ColouringsBrewster; Noel✭1Coloring » Vertex coloringJon Noel
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Coloring » Vertex coloringJon Noel
Melnikov's valency-variety problemMelnikov✭0Coloring » Vertex coloringasp
Earth-Moon ProblemRingel✭✭1Coloring » Vertex coloringfhavet
Acyclic list colouring of planar graphs.Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena✭✭✭0Coloring » Vertex coloringfhavet
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Coloring » Vertex coloringfhavet
Colouring the square of a planar graphWegner✭✭0Coloring » Vertex coloringfhavet
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Coloring » Vertex coloringfhavet
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Coloring » Vertex coloringJon Noel
Choosability of Graph PowersNoel✭✭1Coloring » Vertex coloringJon Noel
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Coloring » Vertex coloringJon Noel
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Coloring » Vertex coloringJon Noel

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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