Home

Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Random stable roommatesMertens✭✭0Graph Theory » Basic G.T. » Matchingsmdevos
Cube-Simplex conjectureKalai✭✭✭0Geometry » Polytopesmdevos
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
Degenerate colorings of planar graphsBorodin✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Nearly spanning regular subgraphsAlon; Mubayi✭✭✭0Graph Theory » Basic G.T.mdevos
Hedetniemi's ConjectureHedetniemi✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Cores of strongly regular graphsCameron; Kazanidis✭✭✭0Graph Theory » Algebraic G.T.mdevos
Complete bipartite subgraphs of perfect graphsFox✭✭0Graph Theory » Basic G.T.mdevos
Coloring random subgraphsBukh✭✭0Graph Theory » Probabilistic G.T.mdevos
4-regular 4-chromatic graphs of high girthGrunbaum✭✭0Graph Theory » Coloringmdevos
Characterizing (aleph_0,aleph_1)-graphsDiestel; Leader✭✭✭0Graph Theory » Infinite Graphsmdevos
Negative association in uniform forestsPemantle✭✭0Graph Theory » Probabilistic G.T.mdevos
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Counting 3-colorings of the hex latticeThomassen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Non-edges vs. feedback edge sets in digraphsChudnovsky; Seymour; Sullivan✭✭✭0Graph Theory » Directed Graphsmdevos
Monochromatic reachability in edge-colored tournamentsErdos✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Monochromatic reachability or rainbow trianglesSands; Sauer; Woodrow✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Simplexity of the n-cube✭✭✭1Geometrymdevos
Sum-product problemErdos; Szemeredi✭✭✭0Number Theorymdevos
Circular colouring the orthogonality graphDeVos; Ghebleh; Goddyn; Mohar; Naserasr✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Seymour's r-graph conjectureSeymour✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Goldberg's conjectureGoldberg✭✭✭0Graph Theory » Coloring » Edge coloringmdevos
Edge-antipodal colorings of cubesNorine✭✭0Combinatorics » Ramsey Theorymdevos
Termination of the sixth Goodstein SequenceGraham✭0Unsortedmdevos
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
Does the chromatic symmetric function distinguish between trees?Stanley✭✭0Graph Theory » Algebraic G.T.mdevos
Inequality of the means✭✭✭0Geometrymdevos
Domination in plane triangulationsMatheson; Tarjan✭✭0Graph Theory » Topological G.T.mdevos
Graphs with a forbidden induced tree are chi-boundedGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Are vertex minor closed classes chi-bounded?Geelen✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Domination in cubic graphsReed✭✭0Graph Theory » Basic G.T.mdevos
Crossing numbers and coloringAlbertson✭✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
A gold-grabbing gameRosenfeld✭✭0Graph Theory » Graph Algorithmsmdevos
Friendly partitionsDeVos✭✭0Graph Theory » Basic G.T.mdevos
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Edge Reconstruction ConjectureHarary✭✭✭0Graph Theorymelch
trace inequality✭✭0AlgebraMiwa Lin
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
Are there infinitely many counter examples for the GoldBach Conjecture? Is it impossible to find that out?Nguyen✭✭0Logicnamducnguyen
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
Seymour's Second Neighbourhood ConjectureSeymour✭✭✭1Graph Theory » Directed Graphsnkorppi
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
3 month loans option @ http://e-24hourloans.co.uk✭✭0Algebrapeeterjhn
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Is every regular paratopological group Tychonoff?unknown✭✭0Topologyporton
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Pseudodifference of filter objectsPorton✭✭0Unsortedporton

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