Home » Subject

Graph Theory


TitleAuthor(s)Imp.¹Rec.²Topic » Subtopicsort iconPosted by
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Coloring » Vertex coloringJon Noel
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Coloring » Vertex coloringDavid Wood
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Coloring » Vertex coloringJon Noel
The Two Color ConjectureNeumann-Lara✭✭0Directed Graphsmdevos
Woodall's ConjectureWoodall✭✭✭0Directed Graphsmdevos
The Bermond-Thomassen ConjectureBermond; Thomassen✭✭0Directed GraphsJS
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Directed Graphsnkorppi
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Directed Graphsmdevos
Oriented trees in n-chromatic digraphsBurr✭✭✭0Directed Graphsfhavet
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
Splitting a digraph with minimum outdegree constraintsAlon✭✭✭0Directed Graphsfhavet
Long directed cycles in diregular digraphsJackson✭✭✭0Directed Graphsfhavet
Arc-disjoint out-branching and in-branchingThomassen✭✭0Directed Graphsfhavet
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Directed Graphsfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Directed Graphsfhavet
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Directed Graphsfhavet
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Directed Graphsfhavet
Cyclic spanning subdigraph with small cyclomatic numberBondy✭✭0Directed Graphsfhavet
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Directed Graphsfhavet
Erdős-Posa property for long directed cyclesHavet; Maia✭✭0Directed Graphsfhavet
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Directed Graphsfhavet
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Directed Graphs » Tournamentsmdevos
Decomposing an even tournament in directed paths.Alspach; Mason; Pullman✭✭✭0Directed Graphs » Tournamentsfhavet
Edge-disjoint Hamilton cycles in highly strongly connected tournaments.Thomassen✭✭0Directed Graphs » Tournamentsfhavet
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Directed Graphs » Tournamentsfhavet
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Directed Graphs » Tournamentsfhavet
The Erdös-Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.mdevos
What is the smallest number of disjoint spanning trees made a graph HamiltonianGoldengorin✭✭0Extremal G.T.boris
Extremal problem on the number of tree endomorphismZhicong Lin✭✭1Extremal G.T.shudeshijie
Complexity of the H-factor problem.Kühn; Osthus✭✭0Extremal G.T.fhavet
Odd-cycle transversal in triangle-free graphsErdos; Faudree; Pach; Spencer✭✭0Extremal G.T.fhavet
Triangle-packing vs triangle edge-transversal.Tuza✭✭0Extremal G.T.fhavet
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Extremal G.T.asp
Weak saturation of the cube in the cliqueMorrison; Noel✭1Extremal G.T.Jon Noel
Multicolour Erdős--Hajnal ConjectureErdos; Hajnal✭✭✭0Extremal G.T.Jon Noel
The stubborn list partition problemCameron; Eschen; Hoang; Sritharan✭✭0Graph Algorithmsmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Algorithmsmdevos
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Algorithmsfhavet
Ryser's conjectureRyser✭✭✭0Hypergraphsmdevos
¿Are critical k-forests tight?Strausz✭✭0HypergraphsDino
Frankl's union-closed sets conjectureFrankl✭✭0Hypergraphstchow
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Hypergraphsfhavet
Turán's problem for hypergraphsTuran✭✭0Hypergraphsfhavet
Seymour's self-minor conjectureSeymour✭✭✭0Infinite Graphsmdevos
Unions of triangle free graphsErdos; Hajnal✭✭✭0Infinite Graphsmdevos
Infinite uniquely hamiltonian graphsMohar✭✭0Infinite GraphsRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Infinite GraphsRobert Samal

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