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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » SubtopicPosted bysort icon
Linial-Berge path partition dualityBerge; Linial✭✭✭0Graph Theory » Coloringberger
Strong colorabilityAharoni; Alon; Haxell✭✭✭0Graph Theory » Coloring » Vertex coloringberger
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Minimal graphs with a prescribed number of spanning treesAzarija; Skrekovski✭✭1Graph Theoryazi
Melnikov's valency-variety problemMelnikov✭0Graph Theory » Coloring » Vertex coloringasp
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
Strong 5-cycle double cover conjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theory » Basic G.T. » Cyclesarthur
3-Decomposition ConjectureArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
Cycle Double Covers Containing Predefined 2-Regular SubgraphsArthur; Hoffmann-Ostenhof✭✭✭0Graph Theoryarthur
3-Edge-Coloring ConjectureArthur; Hoffmann-Ostenhof✭✭✭1Graph Theoryarthur
Bounding the chromatic number of triangle-free graphs with fixed maximum degreeKostochka; Reed✭✭0Graph Theory » Coloring » Vertex coloringAndrew King
Covering powers of cycles with equivalence subgraphs✭0Graph TheoryAndrew King
Obstacle number of planar graphsAlpert; Koch; Laison✭1Graph TheoryAndrew King
The Borodin-Kostochka ConjectureBorodin; Kostochka✭✭0Graph TheoryAndrew King
Criterion for boundedness of power seriesRüdinger✭1Analysisandreasruedinger
Asymptotic Distribution of Form of Polyhedra Rüdinger✭✭0Graph Theory » Basic G.T.andreasruedinger
Geodesic cycles and Tutte's TheoremGeorgakopoulos; Sprüssel✭✭1Graph Theory » Basic G.T. » CyclesAgelos
End-Devouring RaysGeorgakopoulos✭1Graph Theory » Infinite GraphsAgelos
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Erdős–Straus conjectureErdos; Straus✭✭1Number TheoryACW
Convex uniform 5-polytopes✭✭1GeometryACW
Complexity of square-root sumGoemans✭✭0Theoretical Comp. Sci. » Complexityabie

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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