Sintiari and Trotignon's logarithmic-treewidth conjecture for even-hole-free graphs

For a graph $G=(V(G),E(G))$, let $\operatorname{tw}(G)$ denote its treewidth, defined as the minimum width of a tree decomposition, where the width is the maximum bag size minus one. A hole is an induced cycle with at least four vertices, and an even-hole-free graph has no hole of even length. A clique is a set of pairwise adjacent vertices. Sintiari and Trotignon's conjecture. For every integer $t$, there exists a constant $c_t$ such that every even-hole-free graph $G$ with no clique of size $t$ satisfies

$$\operatorname{tw}(G)\leq c_t\log |V(G)|.$$

This conjecture seeks a logarithmic upper bound on treewidth in terms of the number of vertices for even-hole-free graphs with bounded clique number, reflecting the paper's aim of establishing logarithmic treewidth under such structural restrictions. Its resolution status is not specified in the supplied source material.