Abyazi Sani–Alishahi conjecture for deleted Kneser hypergraphs

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Let A⊂[n]A\subset[n], and let KGAr(n,k)\mathrm{KG}^r_A(n,k) be the subhypergraph of the rr-uniform Kneser hypergraph induced by the kk-subsets σ⊂[n]\sigma\subset[n] with σ⊄A\sigma\not\subset A. Abyazi Sani–Alishahi's conjecture. If n≥2rkn\ge 2rk, then

χ(KGAr(n,k))=⌈n−max⁡{r(k−1),∣A∣}r−1⌉.\chi\bigl(\mathrm{KG}^r_A(n,k)\bigr)=\left\lceil\frac{n-\max\{r(k-1),|A|\}}{r-1}\right\rceil.

The source identifies this as a conjecture of Abyazi Sani and Alishahi and does not state a general resolution.

References

Primary source

Jai Aslam, Shuli Chen, Ethan Coldren, Florian Frick and Linus Setiabrata, “On the generalized Erdős–Kneser conjecture: proofs and reductions”, arXiv:1712.03456 (2017).

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