
orthogonality
The Double Cap Conjecture ★★
Author(s): Kalai
Conjecture The largest measure of a Lebesgue measurable subset of the unit sphere of
containing no pair of orthogonal vectors is attained by two open caps of geodesic radius
around the north and south poles.


Keywords: combinatorial geometry; independent set; orthogonality; projective plane; sphere
Circular colouring the orthogonality graph ★★
Author(s): DeVos; Ghebleh; Goddyn; Mohar; Naserasr
Let denote the graph with vertex set consisting of all lines through the origin in
and two vertices adjacent in
if they are perpendicular.
Problem Is
?

Keywords: circular coloring; geometric graph; orthogonality
