7 problems

Let $n$-leaved phylogenetic trees be compared using the quartet distance, whose diameter is the maximum distance between two such trees. Bandelt–Dress conjecture. The diameter is a…

Let $T\in\widehat{\mathcal{RBT}}_n$ be a fixed phylogenetic tree, and let $T'$ be a random tree differing from $T$ by a single subtree-prune-and-regraft (SPR) move, chosen uniforml…

Let $N(B)$ be a tree-metrizable minimal support network of a biconnected component $B$, and suppose that $N(B)$ has $n$ leaves. A reticulation arc is an arc entering a reticulation…

Let $N$ be a level-$k$ HGT network with a biconnected component $B$. Let $N(B)$ denote the minimal support network of $B$, let $T_{N(B)}$ denote its underlying tree, and call a pai…

Let $V$ be a finite vertex set, let $K_V$ be the complete graph on $V$, let $r$ be an edge-connectivity requirement, and let $g \colon E(K_V) \rightarrow \mathbb{Z}_+$ be a capacit…

Let $\mathcal T_n$ be the space of unrooted trees on $n$ labelled leaves, equipped with the tree distance under consideration. A caterpillar is an unrooted tree whose internal vert…

Let ${\mathcal M}=(M,\rho)$ be a finite metric space. For a tree $G$ connecting $M$, let ${\mathcal O}(M,G)$ be the set of tours of $M$ with respect to $G$, and for each…