On the integrality ratio of the subtour LP for Euclidean TSP

A long standing conjecture says that the integrality ratio of the subtour LP for metric TSP is 4/34/3. A well known family of graphic TSP instances achieves this lower bound asymptotically. For Euclidean TSP the best known lower bound on the integrality ratio was 8/78/7. We improve this value by presenting a family of Euclidean TSP instances for which the integrality ratio of the subtour LP converges to 4/3.