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Hall-Paige conjectureHall; Paige✭✭✭0Group Theorymdevos
Bounding the chromatic number of graphs with no odd holeGyarfas✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
(2 + epsilon)-flow conjectureGoddyn; Seymour✭✭✭0Graph Theory » Coloring » Nowhere-zero flowsmdevos
The sum of the two largest eigenvaluesGernert✭✭0Graph Theory » Algebraic G.T.mdevos
Fowler's Conjecture on eigenvalues of (3,6)-polyhedraFowler✭✭0Graph Theory » Algebraic G.T.Robert Samal
Monochromatic reachability in edge-colored tournamentsErdos✭✭✭0Graph Theory » Directed Graphs » Tournamentsmdevos
Middle levels problemErdos✭✭0Graph Theory » Basic G.T. » Cyclestchow
Good edge labeling and girthBode-Farzad-Theis✭✭0Graph Theory » Coloring » LabelingDOT
Alon-Saks-Seymour ConjectureAlon; Saks; Seymour✭✭✭0Graph Theory » Coloring » Vertex coloringmdevos
Bounded colorings for planar graphsAlon; Ding; Oporowski; Vertigan✭✭1Graph Theory » Topological G.T. » Coloringmdevos
Nonrepetitive colourings of planar graphsAlon N.; Grytczuk J.; Hałuszczak M.; Riordan O.✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Total Domination number of a hypercubeAdel P. Kazemi✭✭✭0Graph Theory » Basic G.T.Adel P. Kazemi
Total Dominator Chromatic Number of a HypercubeAdel P. Kazemi✭✭0Graph Theory » Coloring » Vertex coloringAdel P. Kazemi
Decomposing the truncated octahedron into parallelepipeds✭1Geometry » Polytopesmdevos
Bigger cycles in cubic graphs✭✭0Graph Theory » Basic G.T. » Cyclesmdevos
On Gersgorin Theorem✭✭0AlgebraMiwa Lin
Inequality of complex numbers✭✭1Analysisfeanor
spanning trees✭✭1Graph Theoryakhodkar
Oakley sunglasses can successfully secure their sight will very likely be common-sense✭✭0Analysishaumiki
Steinberg's conjecture✭✭✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Choice number of complete multipartite graphs with parts of size 4✭1Graph Theory » Coloring » Vertex coloringJon Noel
DIS-PROOF OF BEALS CONJECTURE✭✭✭0Number Theory » Additive N.T.lalitha

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