3 problems

Let $\mathcal S$ be a split system on a set $X$ with $|X|\geq 3$. A split system is bijective when it is both injective and surjective: distinct three-element subsets of $X$ have d…

Compatibility conjecture. $\mathfrak S$ is compatible if and only if every submultiset of $\mathfrak S$ of size at most $\Delta(\mathcal M)+2$ is compatible.

Spillner's conjecture. Recognizing whether a split system is flat is NP-hard.