4 problems

Odd-bridge conjecture. If the bridge of $T$ has odd length, then no maximal non-bipartite arrangement is a maximum arrangement; equivalently,

Slow-decay conjecture. The proportion decays according to

Weak bipartition conjecture. The same limiting assertion as in the strong bipartition conjecture holds with merely $c>0$; equivalently, the asymptotic proportion is positive.

Strong bipartition conjecture. The limit exists and is a positive constant: