Home

Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
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; Noel✭1Graph Theory » Coloring » Vertex coloringJon Noel
Choice Number of k-Chromatic Graphs of Bounded OrderNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Melnikov's valency-variety problemMelnikov✭0Graph 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
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
The Two Color ConjectureNeumann-Lara✭✭0Graph Theory » Directed Graphsmdevos
Woodall's ConjectureWoodall✭✭✭0Graph Theory » Directed Graphsmdevos
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Graph Theory » Directed GraphsJS
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
Oriented trees in n-chromatic digraphsBurr✭✭✭0Graph Theory » Directed Graphsfhavet
Antidirected trees in digraphsAddario-Berry; Havet; Linhares Sales; Reed; Thomassé✭✭0Graph Theory » Directed Graphsfhavet
Directed path of length twice the minimum outdegreeThomassé✭✭✭0Graph Theory » Directed Graphsfhavet
Caccetta-Häggkvist ConjectureCaccetta; Häggkvist✭✭✭✭0Graph Theory » Directed Graphsfhavet
Ádám's ConjectureÁdám✭✭✭0Graph Theory » Directed Graphsfhavet
Splitting a digraph with minimum outdegree constraintsAlon✭✭✭0Graph Theory » Directed Graphsfhavet
Long directed cycles in diregular digraphsJackson✭✭✭0Graph Theory » Directed Graphsfhavet
Arc-disjoint out-branching and in-branchingThomassen✭✭0Graph Theory » Directed Graphsfhavet
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Graph Theory » Directed Graphsfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Graph Theory » Directed Graphsfhavet
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Graph Theory » Directed Graphsfhavet
Cyclic spanning subdigraph with small cyclomatic numberBondy✭✭0Graph Theory » Directed Graphsfhavet
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Graph Theory » Directed Graphsfhavet
Erdős-Posa property for long directed cyclesHavet; Maia✭✭0Graph Theory » Directed Graphsfhavet
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphsfhavet
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Decomposing an even tournament in directed paths.Alspach; Mason; Pullman✭✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Edge-disjoint Hamilton cycles in highly strongly connected tournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Graph Theory » Extremal G.T.mdevos
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Graph Theory » Extremal G.T.boris
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Graph Theory » Extremal G.T.shudeshijie
Complexity of the H-factor problem.Kühn; Osthus✭✭0Graph Theory » Extremal G.T.fhavet
Odd-cycle transversal in triangle-free graphsErdos; Faudree; Pach; Spencer✭✭0Graph Theory » Extremal G.T.fhavet
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Graph Theory » Extremal G.T.fhavet
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

Syndicate content