Graph Theory


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Earth-Moon ProblemRingel✭✭1Coloring » 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
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
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0mdevos
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Coloring » Vertex coloringJon Noel
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-Posa property for long directed cyclesHavet; Maia✭✭0Directed Graphsfhavet
Choosability of Graph PowersNoel✭✭1Coloring » Vertex coloringJon Noel
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Basic G.T.mhaythorpe
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
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1David Wood
Forcing a 2-regular minorReed; Wood✭✭1Basic G.T. » MinorsDavid Wood
Nonrepetitive colourings of planar graphsAlon N.; Grytczuk J.; Hałuszczak M.; Riordan O.✭✭0Coloring » Vertex coloringDavid Wood
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Coloring » Vertex coloringJon Noel
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
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 circular embedding conjectureHaggard✭✭✭0Basic G.T. » Cyclesmdevos
(m,n)-cycle coversCelmins; Preissmann✭✭✭0Basic G.T. » Cyclesmdevos
Faithful cycle coversSeymour✭✭✭0Basic G.T. » Cyclesmdevos
Decomposing eulerian graphs✭✭✭0Basic G.T. » Cyclesmdevos
Petersen coloring conjectureJaeger✭✭✭0Coloring » Edge coloringmdevos
Highly connected graphs with no K_n minorThomas✭✭✭0Basic G.T. » Minorsmdevos
Jorgensen's ConjectureJorgensen✭✭✭0Basic G.T. » Minorsmdevos
57-regular Moore graph?Hoffman; Singleton✭✭✭0Algebraic G.T.mdevos
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