The two-point Fano and ideal binary clutters.

*(English)*Zbl 1449.05041In this paper, necessary conditions for a binary clutter to be non-ideal are obtained. By that, the authors prove the weakened version of the flowing conjecture. Moreover, it is shown that for each element \(e\) of the ground set at least one member of a blocking pair of minimally non-ideal binary clutters has a two-point Fano minor going through \(e\), in the case when the both members of the blocking pair don’t comprise sets with cardinality 3. The proof is based on the concept of a strict \(e\)-hub.

Reviewer: Svetlana A. Kravchenko (Minsk)