Graph Theory


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Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour.Sabidussi✭✭0Basic G.T. » Cyclesfhavet
Partition of a cubic 3-connected graphs into paths of length 2.Kelmans✭✭0Basic G.T. » Pathsfhavet
Lovász Path Removal ConjectureLovasz✭✭0fhavet
Large induced forest in a planar graph.Abertson; Berman✭✭0Topological G.T.fhavet
Subdivision of a transitive tournament in digraphs with large outdegree. Mader✭✭0Directed Graphsfhavet
Turán number of a finite family.Erdos; Simonovits✭✭0fhavet
Subgraph of large average degree and large girth.Thomassen✭✭0Basic G.T.fhavet
Complexity of the H-factor problem.Kühn; Osthus✭✭0Extremal G.T.fhavet
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Hypergraphsfhavet
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
Acyclic list colouring of planar graphs.Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena✭✭✭0Coloring » Vertex coloringfhavet
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Topological G.T.fhavet
Switching reconstruction conjectureStanley✭✭0fhavet
Switching reconstruction of digraphsBondy; Mercier✭✭0fhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Directed Graphsfhavet
Edge-disjoint Hamilton cycles in highly strongly connected tournaments.Thomassen✭✭0Directed Graphs » Tournamentsfhavet
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Directed Graphsfhavet
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Basic G.T. » Cyclesfhavet
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Basic G.T. » Cyclesfhavet
Turán's problem for hypergraphsTuran✭✭0Hypergraphsfhavet
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Basic G.T. » Cyclesfhavet
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
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Directed Graphs » Tournamentsfhavet
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Algorithmsfhavet
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Directed Graphs » Tournamentsfhavet
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Extremal G.T.asp
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0mdevos
Are almost all graphs determined by their spectrum?✭✭✭0mdevos
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Directed Graphsfhavet
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0fhavet
Cyclic spanning subdigraph with small cyclomatic numberBondy✭✭0Directed Graphsfhavet
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Directed Graphsfhavet
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
Imbalance conjectureKozerenko✭✭0Sergiy Kozerenko
Nonrepetitive colourings of planar graphsAlon N.; Grytczuk J.; Hałuszczak M.; Riordan O.✭✭0Coloring » Vertex coloringDavid Wood
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Coloring » Vertex coloringDavid Wood
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0David Wood
Circular flow number of regular class 1 graphsSteffen✭✭0Coloring » Nowhere-zero flowsEckhard Steffen
Circular flow numbers of $r$-graphsSteffen✭✭0Eckhard Steffen
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Coloring » Vertex coloringJon Noel
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0arthur
Monochromatic reachability in arc-colored digraphsSands; Sauer; Woodrow✭✭✭0Directed Graphsfhavet
Cycle Double Covers Containing Predefined 2-Regular SubgraphsArthur; Hoffmann-Ostenhof✭✭✭0arthur
What is the largest graph of positive curvature?DeVos; Mohar1Topological G.T. » Planar graphsmdevos
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