Hypergraph criteria for non-pathological ideals

Identify hypergraph-theoretic properties that determine when the ideal generated by the complete and independent sets of a hypergraph is non-pathological.

Background

The paper relates the non-triviality and pathology of coloring ideals to chromatic properties of associated hypergraphs. It states that these relations are not fully understood and asks whether hypergraph properties can determine non-pathology.

References

Question 5.22. Are there hypergraph-theoretical properties that determine when the ideal generated by a hypergraph (through its complete and independent sets) is non-pathological?

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in Question 5.22, p. 28