Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Turán number of a finite family.Erdos; Simonovits✭✭0Graph Theoryfhavet
Subgraph of large average degree and large girth.Thomassen✭✭0Graph Theory » Basic G.T.fhavet
Complexity of the H-factor problem.Kühn; Osthus✭✭0Graph Theory » Extremal G.T.fhavet
Simultaneous partition of hypergraphsKühn; Osthus✭✭0Graph Theory » Hypergraphsfhavet
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
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
Steinberg's conjecture✭✭✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Every 4-connected toroidal graph has a Hamilton cycleGrunbaum; Nash-Williams✭✭0Graph Theory » Topological G.T.fhavet
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Switching reconstruction of digraphsBondy; Mercier✭✭0Graph Theoryfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Graph Theory » Directed Graphsfhavet
Edge-disjoint Hamilton cycles in highly strongly connected tournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
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
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
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
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
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
Erdös-Posa property for long directed cycles.Havet; Maia✭✭0Graph Theory » Directed Graphsfhavet
Distribution and upper bound of mimic numbersBhattacharyya✭✭1Number Theory » Analytic N.T.facility_cttb@i...
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
The Riemann HypothesisRiemann✭✭✭✭0Number Theory » Analytic N.T.eric
Good Edge LabelingsAraújo; Cohen; Giroire; Havet✭✭0Graph Theory » Coloring » LabelingDOT
Extension complexity of (convex) polygons✭✭0Geometry » PolytopesDOT
Chromatic number of random lifts of complete graphsAmit✭✭0Graph Theory » Probabilistic G.T.DOT
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Durer's ConjectureDurer; Shephard✭✭✭1Geometry » Polytopesdmoskovich
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
¿Are critical k-forests tight?Strausz✭✭0Graph Theory » HypergraphsDino
Exponential Algorithms for KnapsackLipton✭✭1Theoretical Comp. Sci. » Algorithmsdick lipton
Double-critical graph conjectureErdos; Lovasz✭✭0Graph Theory » Coloring » Vertex coloringDFR
Average diameter of a bounded cell of a simple arrangementDeza; Terlaky; Zinchenko✭✭0Geometrydeza
Continous analogue of Hirsch conjectureDeza; Terlaky; Zinchenko✭✭0Geometry » Polytopesdeza
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
Syndicate content