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arXiv · 2606.16109

Large Independent Sets in Flag Spheres

Varun Shah
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Abstract

For every $d \geq 4$, we construct a family of $(d-1)$-dimensional flag simplicial spheres $\mathcal K_n$ whose graphs contain independent sets of size asymptotically equal to the number of vertices. More precisely, we prove that for sufficiently large $n$, $$ α(G(\mathcal K_n)) \geq f_0(\mathcal K_n) - \frac{C\,f_0(\mathcal K_n)}{\left(\log f_0(\mathcal K_n)\right)^{\lfloor d/2 \rfloor-1}},$$ where $C = C(d) > 0$. This disproves a recent conjecture of Chudnovsky and Nevo.

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Varun Shah. 2026-06-28. Large Independent Sets in Flag Spheres. https://arxiv.org/abs/2606.16109

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