and matroid intersection, which incorporated the techniques of Mömke and Svensson, and improved the approximation ratio to $7/5$, where it currently stands [@sebHo2012shorter]. For the special case of $k$-regular graphs, Vishnoi gave an algorithm for graph-TSP with an approximation guarantee that approaches 1 as $k$ increases [@vishnoi2012permanent].

Some of the new techniques for graph-TSP have also lead to progress on the metric $s$-$t$-path TSP, in which the goal is to find a path between two fixed vertices that visits every vertex at least once. Mömke and Svensson applied their techniques to the $s$-$t$-path graph-TSP for which they obtained a 1.586-approximation algorithm, improving on the previously best-known bound of $5/3$ due to Hoogeveen [@hoogeveen]. Mucha improved this ratio slightly to $19/12$ [@DBLP:conf/stacs/Mucha12]. §and Vygen gave a $3/2$-approximation algorithm for $s$-$t$-path graph-TSP, which matches the integrality gap of the standard linear programming relaxation for this problem [@sebHo2012shorter]. Even more recently, Gao gave another, extremely elegant, $3/2$-approximation for this problem [@gao2013lp]. His result was based on ideas introduced for the $s$-$t$-path TSP in general metrics by An et al. who gave a 1.618 approximation for this problem [@an2012improving], improving on the algorithm of Hoogeveen [@hoogeveen]. §improved the approximation ratio for the $s$-$t$-path TSP 