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Anders Bj¨ orner, Andreas Paffenholz, Jonas Sj¨ ostrand, G¨ unter M · 2005

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Sharp Bounds on the Independence Number of Simplicial Spheres

math.CO · 2026-08-06 · accept · novelty 7.0

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.

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  • Sharp Bounds on the Independence Number of Simplicial Spheres math.CO · 2026-08-06 · accept · none · ref 5

    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.