  We present a $1.5$-approximation for the Metric Path Traveling Salesman
Problem (Path TSP). All recent improvements on Path TSP crucially exploit a
structural property shown by An, Kleinberg, and Shmoys [Journal of the ACM,
2015], namely that narrow cuts with respect to a Held-Karp solution form a
chain. We significantly deviate from these approaches by showing the benefit of
dealing with larger $s$-$t$ cuts, even though they are much less structured.
More precisely, we show that a variation of the dynamic programming idea
recently introduced by Traub and Vygen [SODA, 2018] is versatile enough to deal
with larger size cuts, by exploiting a seminal result of Karger on the number
of near-minimum cuts. This avoids a recursive application of dynamic
programming as used by Traub and Vygen, and leads to a considerably simpler
algorithm avoiding an additional error term in the approximation guarantee. We
match the still unbeaten $1.5$-approximation guarantee of Christofides'
algorithm for TSP. Hence, any further progress on the approximability of Path
TSP will also lead to an improvement for TSP.
