Chudnovsky–Nevo conjecture on independent sets in flag spheres

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Let α(n,d)\alpha(n,d) denote the minimum size of the largest independent set among all flag triangulations of dd-spheres on nn vertices.

Chudnovsky–Nevo conjecture.

α(n,d)=⌈n+d−22d⌉.\alpha(n,d)=\left\lceil\frac{n+d-2}{2d}\right\rceil.

This conjecture gives a sharp linear lower bound for independent sets in flag triangulations of spheres, motivated by the study of their ff-vectors. Its resolution status is not specified in the supplied source.

References

Primary source

Andrew Newman, “Chromatic numbers of flag 3-spheres”, arXiv:2311.08499 (2023).

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