The two-disjoint-triangles conjecture for maximum subtour-LP integrality ratio instances

Let an instance have a fixed number of vertices, and let $x^*$ be an optimal fractional solution of its subtour LP. The two-disjoint-triangles conjecture. The instances maximizing the integrality ratio among all instances with a fixed number of vertices have the following structure: $x^*(e)=\frac{1}{2}$ for all edges $e$ of two disjoint triangles, and $x^*(e)=0$ or $x^*(e)=1$ for all other edges $e$. The conjecture proposes a common structural form for extremal instances, extending the structures observed computationally for small numbers of vertices; whether it holds for every fixed number of vertices is not established in the supplied text.