Geometry

Kneser–Poulsen conjecture ★★★

Author(s): Kneser; Poulsen

Conjecture   If a finite set of unit balls in $ \mathbb{R}^n $ is rearranged so that the distance between each pair of centers does not decrease, then the volume of the union of the balls does not decrease.

Keywords: pushing disks

Posted by tchow
updated September 25th, 2008
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Combinatorics

Wide partition conjecture ★★

Author(s): Chow; Taylor

Conjecture   An integer partition is wide if and only if it is Latin.

Keywords:

Posted by tchow
updated September 24th, 2008
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Graph Theory » Coloring » Vertex coloring

Circular colouring the orthogonality graph ★★

Author(s): DeVos; Ghebleh; Goddyn; Mohar; Naserasr

Let $ {\mathcal O} $ denote the graph with vertex set consisting of all lines through the origin in $ {\mathbb R}^3 $ and two vertices adjacent in $ {\mathcal O} $ if they are perpendicular.

Problem   Is $ \chi_c({\mathcal O}) = 4 $?

Keywords: circular coloring; geometric graph; orthogonality

Posted by mdevos
updated September 28th, 2009
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