Infinitely Many Almost-Uniform 3-Qualitative Independence Hypergraphs are Cores

@misc{thomas2026infinitely,
  title = {{Infinitely Many Almost-Uniform 3-Qualitative Independence Hypergraphs are Cores}},
  author = {Raina Mary Thomas and Yasmeen Akhtar},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04384},
  eprint = {2611.04384},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04384},
}

TY  - UNPB
TI  - Infinitely Many Almost-Uniform 3-Qualitative Independence Hypergraphs are Cores
AU  - Raina Mary Thomas
AU  - Yasmeen Akhtar
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04384
UR  - https://arxiv.org/abs/2611.04384
AB  - Qualitative independence is a property associated with the column vectors of well-known combinatorial designs known as covering arrays and qualitative independence hypergraphs characterize the existence of covering arrays on hypergraphs. The core of a hypergraph H is an interesting structural characteristic to study, as it is the unique (up to isomorphism), minimal subhypergraph H^• ⊆ H which is homomorphically equivalent to H. We use the vertex transitivity and strong independence number of almost-uniform $3$-qualitative independence hypergraphs, 3−AUQI(2n+1,2), to show that 3−AUQI(2n+1,2) are cores for infinitely many n. Consequently, we establish that 3−QI(9,2) is a core and also obtain a lower bound on the strong chromatic number of $3$-qualitative independence hypergraphs 3−QI(2n+1,2).
ER  -