5 problems

McCarty's conjecture. The tree-length of $G$ is small if and only if its McCarty-width is small.

Let $G$ be a graph, and let $\lambda(G)$ denote the length of its longest induced cycle. Dourisboure–Gavoille's tree-length bound conjecture. The tree-length satisfies … Dourisbour…

Let $G$ be a graph with tree-length $tl(G)$, and let $(T_i,\phi_i)$, $H_i$, $S_i$, $B_k(x_i)$, and property $P_i$ be as in the $(k,\ell)$-Disk Tree algorithm. Suppose that…

Let $G$ be a graph with tree-length $tl(G)$, and let $(k,\ell)$-Disk Tree denote the algorithm described in the paper, with parameters $k$ and $\ell$. Dourisboure–Gavoille's refine…

Let $G$ be a graph, and let $tl(G)$ denote its tree-length. The $k$-disk-tree algorithm is the algorithm that constructs a tree decomposition using parameter $k$. Dourisboure–Gavoi…