For fixed d at least 4, the maximum independence number of a (d-1)-sphere on n vertices is n minus Theta(n^{1/floor(d/2)}); for flag 4- and 5-spheres it is n minus Theta(sqrt(n)), and Bier spheres have independence number at most half their vertices.
Upper bound theorem for odd-dimensional flag triangulations of manifolds.Mathematika, 62(3):909–928, 2016
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2026 1verdicts
ACCEPT 1roles
background 1polarities
support 1representative citing papers
citing papers explorer
-
Sharp Bounds on the Independence Number of Simplicial Spheres
For fixed d at least 4, the maximum independence number of a (d-1)-sphere on n vertices is n minus Theta(n^{1/floor(d/2)}); for flag 4- and 5-spheres it is n minus Theta(sqrt(n)), and Bier spheres have independence number at most half their vertices.