Open Problems


TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Graph Theory » Coloring » Vertex coloringberger
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
Grunbaum's ConjectureGrunbaum✭✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Woodall's ConjectureWoodall✭✭✭0Graph Theory » Directed Graphsmdevos
A generalization of Vizing's Theorem?Rosenfeld✭✭0Graph Theory » Coloring » Edge coloringmdevos
The Crossing Number of the Complete Graph✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the Complete Bipartite GraphTuran✭✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
The Crossing Number of the HypercubeErdos; Guy✭✭0Graph Theory » Topological G.T. » Crossing numbersRobert Samal
Fat 4-polytopesEppstein; Kuperberg; Ziegler✭✭✭0Geometry » Polytopesmdevos
Drawing disconnected graphs on surfacesDeVos; Mohar; Samal✭✭0Graph Theory » Topological G.T. » Crossing numbersmdevos
Antichains in the cycle continuous orderDeVos✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Seymour's self-minor conjectureSeymour✭✭✭0Graph Theory » Infinite Graphsmdevos
Reed's omega, delta, and chi conjectureReed✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Gao's theorem for nonabelian groupsDeVos✭✭0Number Theory » Combinatorial N.T.mdevos
Triangle free strongly regular graphs✭✭✭0Graph Theory » Algebraic G.T.mdevos
Half-integral flow polynomial valuesMohar✭✭0Graph Theory » Algebraic G.T.mohar
Unions of triangle free graphsErdos; Hajnal✭✭✭0Graph Theory » Infinite Graphsmdevos
Diagonal Ramsey numbersErdos✭✭✭✭0Combinatorics » Ramsey Theorymdevos
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
Bases of many weightsSchrijver; Seymour✭✭✭0Combinatorics » Matroid Theorymdevos
Ramsey properties of Cayley graphsAlon✭✭✭0Graph Theory » Algebraic G.T.mdevos
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
Aharoni-Berger conjectureAharoni; Berger✭✭✭0Combinatorics » Matroid Theorymdevos
Barnette's ConjectureBarnette✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
List colorings of edge-critical graphsMohar✭✭0Graph Theory » Coloring » Edge coloringRobert Samal
Circular coloring triangle-free subcubic planar graphsGhebleh; Zhu✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
Laplacian Degrees of a GraphGuo✭✭0Graph Theory » Algebraic G.T.Robert Samal
5-local-tensionsDeVos✭✭0Graph Theory » Topological G.T. » Coloringmdevos
Mapping planar graphs to odd cyclesJaeger✭✭✭0Graph Theory » Coloring » Homomorphismsmdevos
Sets with distinct subset sumsErdos✭✭✭0Number Theory » Combinatorial N.T.mdevos
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Weak pentagon problemSamal✭✭0Graph Theory » Coloring » HomomorphismsRobert Samal
Graceful Tree Conjecture✭✭✭0Graph Theory » Coloring » Labelingkintali
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
Complexity of square-root sumGoemans✭✭0Theoretical Comp. Sci. » Complexityabie
Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
r-regular graphs are not uniquely hamiltonian.Sheehan✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Infinite uniquely hamiltonian graphsMohar✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in line graphsThomassen✭✭✭0Graph Theory » Basic G.T. » CyclesRobert Samal
Hamiltonian cycles in line graphs of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Hamiltonian cycles in powers of infinite graphsGeorgakopoulos✭✭0Graph Theory » Infinite GraphsRobert Samal
Odd incongruent covering systemsErdos; Selfridge✭✭✭0Number Theory » Combinatorial N.T.Robert Samal
Covering systems with big moduliErdos; Selfridge✭✭0Number Theory » Combinatorial N.T.Robert Samal
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