Geometry » Algebraic Geometry

The Hodge Conjecture ★★★★

Author(s): Hodge

Conjecture   Let $ X $ be a complex projective variety. Then every Hodge class is a rational linear combination of the cohomology classes of complex subvarieties of $ X $.

Keywords: Hodge Theory; Millenium Problems

Posted by Charles
updated July 13th, 2008
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Graph Theory » Directed Graphs » Tournaments

Monochromatic reachability in edge-colored tournaments ★★★

Author(s): Erdos

Problem   For every $ n $, is there a (least) positive integer $ f(n) $ so that whenever a tournament has its edges colored with $ n $ colors, there exists a set $ S $ of at most $ f(n) $ vertices so that every vertex has a monochromatic path to some point in $ S $?

Keywords: digraph; edge-coloring; tournament

Posted by mdevos
updated July 9th, 2008
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