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Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » SubtopicPosted bysort icon
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Coloring » Vertex coloringmdevos
Seymour's r-graph conjectureSeymour✭✭✭0Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Coloring » Edge coloringmdevos
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Algebraic G.T.mdevos
Domination in plane triangulationsMatheson; Tarjan✭✭0Topological G.T.mdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Coloring » Vertex coloringmdevos
Are vertex minor closed classes chi-bounded?Geelen✭✭0Coloring » Vertex coloringmdevos
Domination in cubic graphsReed✭✭0Basic G.T.mdevos
Crossing numbers and coloringAlbertson✭✭✭0Topological G.T. » Crossing numbersmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Algorithmsmdevos
Friendly partitionsDeVos✭✭0Basic G.T.mdevos
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0mdevos
Are almost all graphs determined by their spectrum?✭✭✭0mdevos
Exact colorings of graphsErickson✭✭0Martin Erickson
Monochromatic vertex colorings inherited from Perfect Matchings✭✭✭1Mario Krenn
Universal Steiner triple systemsGrannell; Griggs; Knor; Skoviera✭✭0Coloring » Edge coloringmacajova
Graceful Tree Conjecture✭✭✭0Coloring » Labelingkintali
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Directed GraphsJS
Mixing Circular ColouringsBrewster; Noel✭1Coloring » Vertex coloringJon Noel
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Coloring » Vertex coloringJon Noel
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
Kriesell's ConjectureKriesell✭✭0Basic G.T. » ConnectivityJon Noel
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0ColoringJon Noel
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Coloring » Vertex coloringJon Noel
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Coloring » Vertex coloringJon Noel
Weak saturation of the cube in the cliqueMorrison; Noel✭1Extremal G.T.Jon Noel
Sidorenko's ConjectureSidorenko✭✭✭0Jon Noel
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.Jon Noel
Matchings extend to Hamiltonian cycles in hypercubesRuskey; Savage✭✭1Basic G.T. » MatchingsJirka
Algorithm for graph homomorphismsFomin; Heggernes; Kratsch✭✭0Coloring » Homomorphismsjfoniok
Approximation Ratio for Maximum Edge Disjoint Paths problemBentz✭✭0jcmeyer
Approximation ratio for k-outerplanar graphsBentz✭✭0jcmeyer
Finding k-edge-outerplanar graph embeddingsBentz✭✭0jcmeyer
Partial List ColoringAlbertson; Grossman; Haas✭✭✭0Coloring » Vertex coloringIradmusa
Partial List ColoringIradmusa✭✭✭0Coloring » Vertex coloringIradmusa
Total Colouring ConjectureBehzad✭✭✭0ColoringIradmusa
Vertex Coloring of graph fractional powersIradmusa✭✭✭1Iradmusa
Chromatic number of $\frac{3}{3}$-power of graph✭✭0Iradmusa
Three-chromatic (0,2)-graphsPayan✭✭0ColoringGordon Royle
Odd cycles and low oddness✭✭0Gagik
Oriented trees in n-chromatic digraphsBurr✭✭✭0Directed Graphsfhavet
Decomposing an even tournament in directed paths.Alspach; Mason; Pullman✭✭✭0Directed Graphs » Tournamentsfhavet
Antidirected trees in digraphsAddario-Berry; Havet; Linhares Sales; Reed; Thomassé✭✭0Directed Graphsfhavet
Directed path of length twice the minimum outdegreeThomassé✭✭✭0Directed Graphsfhavet
Caccetta-Häggkvist ConjectureCaccetta; Häggkvist✭✭✭✭0Directed Graphsfhavet
Ádám's ConjectureÁdám✭✭✭0Directed Graphsfhavet
Stable set meeting all longest directed paths.Laborde; Payan; Xuong N.H.✭✭0fhavet

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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