3 problems

Forbidden-pattern characterization conjecture. The ordered matching admits

An ordered $r$-matching is an ordered matching in which every vertex belongs to one of $r$ edge labels, and let $t^{(r)}(n)$ be the minimum, over ordered $r$-matchings of size $n$,…

For each integer $r\geqslant2$, let $t_r^{\operatorname{match}}(n)$ denote the largest size of twins that are unavoidable in every ordered $r$-matching of size $n$. Here twins are…