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In this paper we investigate the integrality ratio of the standard LPrelaxation for the metric $s-t$ Path TSP. We make a near-optimal choice for anauxiliary function used in the analysis of Traub and Vygen which leads to animproved upper bound on the integrality ratio of 1.5273.

Slightly Improved Upper Bound on the Integrality Ratio for the $s-t$ Path TSP