Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Coloring and immersionAbu-Khzam; Langston✭✭✭1Graph Theory » Coloring » Vertex coloringmdevos
Davenport's constant✭✭✭0Number Theory » Combinatorial N.T.mdevos
Rendezvous on a lineAlpern✭✭✭0Unsortedmdevos
Pebbling a cartesian productGraham✭✭✭0Graph Theorymdevos
Coloring the Odd Distance GraphRosenfeld✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Rota's basis conjectureRota✭✭✭0Combinatorics » Matricesmdevos
Even vs. odd latin squaresAlon; Tarsi✭✭✭0Combinatoricsmdevos
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
Universal highly arc transitive digraphsCameron; Praeger; Wormald✭✭✭0Graph Theory » Infinite Graphsmdevos
Unfriendly partitionsCowan; Emerson✭✭✭0Graph Theory » Infinite Graphsmdevos
Strong matchings and coversAharoni✭✭✭0Graph Theory » Infinite Graphsmdevos
Highly arc transitive two ended digraphsCameron; Praeger; Wormald✭✭0Graph Theory » Infinite Graphsmdevos
Ding's tau_r vs. tau conjectureDing✭✭✭0Combinatorics » Optimizationmdevos
Chords of longest cyclesThomassen✭✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
Growth of finitely presented groupsAdyan✭✭✭0Group Theorymdevos
Seagull problemSeymour✭✭✭0Graph Theory » Basic G.T. » Minorsmdevos
Chowla's cosine problemChowla✭✭✭0Number Theorymdevos
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
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 SequenceGraham0Logicmdevos
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
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