Open Problems


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PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Theory » Graph Algorithmsfhavet
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Bounding the on-line choice number in terms of the choice numberZhu✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Sub-atomic product of funcoids is a categorical product✭✭0Algebraporton
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Graph Theory » Directed Graphsfhavet
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0Graph Theoryfhavet
inverse of an integer matrixGregory✭✭0Algebralvoyster
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
Choosability of Graph PowersNoel✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Almost all non-Hamiltonian 3-regular graphs are 1-connectedHaythorpe✭✭1Graph Theory » Basic G.T.mhaythorpe
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
Decomposition of completions of reloidsPorton✭✭0Topologyporton
Every metamonovalued funcoid is monovaluedPorton✭✭0Topologyporton
Every metamonovalued reloid is monovaluedPorton✭✭0Topologyporton
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Graphs of exact colorings✭✭0Algebrasabisood
Dirac's ConjectureDirac✭✭0GeometryDavid Wood
Generalized path-connectedness in proximity spacesPorton✭✭0Topologyporton
Direct proof of a theorem about compact funcoidsPorton✭✭0Topologyporton
Fractional HadwigerHarvey; Reed; Seymour; Wood✭✭1Graph TheoryDavid Wood
Forcing a 2-regular minorReed; Wood✭✭1Graph Theory » Basic G.T. » MinorsDavid Wood
General position subsetsGowers✭✭0GeometryDavid Wood
Nonrepetitive colourings of planar graphsAlon N.; Grytczuk J.; Hałuszczak M.; Riordan O.✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
List Colourings of Complete Multipartite Graphs with 2 Big PartsAllagan✭✭1Graph Theory » Coloring » Vertex coloringJon Noel
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0Graph TheoryDavid Wood
Another conjecture about reloids and funcoidsPorton✭✭0Topologyporton
What are hyperfuncoids isomorphic to?Porton✭✭0Topologyporton
Chromatic number of associahedronFabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood✭✭1GeometryDavid Wood
Circular flow number of regular class 1 graphsSteffen✭✭0Graph Theory » Coloring » Nowhere-zero flowsEckhard Steffen
Circular flow numbers of $r$-graphsSteffen✭✭0Graph TheoryEckhard Steffen
The Double Cap ConjectureKalai✭✭0CombinatoricsJon Noel
Cycles in Graphs of Large Chromatic NumberBrewster; McGuinness; Moore; Noel✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Saturation in the HypercubeMorrison; Noel; Scott✭✭0CombinatoricsJon Noel
Extremal $4$-Neighbour Bootstrap Percolation in the HypercubeMorrison; Noel✭✭0CombinatoricsJon Noel
Turán Problem for $10$-Cycles in the HypercubeErdos✭✭0CombinatoricsJon Noel
Convex Equipartitions with Extreme PerimeterNandakumar✭✭1GeometryNandakumar
Infinite distributivity of meet over join for a principal funcoidPorton✭✭0Topologyporton
A funcoid related to directed topological spacesPorton✭✭0Topologyporton
Outward reloid of composition vs composition of outward reloidsPorton✭✭0Topologyporton
A diagram about funcoids and reloidsPorton✭✭0Topologyporton
Which outer reloids are equal to inner onesPorton✭✭0Topologyporton
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