in general metrics to $8/5$, where it currently stands [@sebHo2013eight].

Mömke-Svensson’s approach to graph-TSP {#sec:MS}
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Christofides’ algorithm for graph-TSP finds a spanning tree of the graph and adds to it a $J$-join, where $J$ is the set of vertices that have odd degree in the spanning tree. Since the spanning tree is connected, the resulting subgraph is clearly connected, and since the $J$-join corrects the parity of the spanning tree, the resulting subgraph is Eulerian. In contrast, the recent approach of Mömke and Svensson is based on removing an odd-join of the graph, which yields a possibly disconnected Eulerian subgraph. Thus, to maintain connectivity, one must double, rather than remove, some of the edges in the odd-join. The key step in proving the approximation guarantee of the algorithm is to show that many edges will actually be removed and relatively few edges will be doubled, resulting in a connected, Eulerian subgraph with few edges. First, Mömke and Svensson design a circulation network, $C(G,T)$, which is constructed based on the input graph $G$, an optimal solution to a linear programming relaxation for graph-TSP, and a carefully chosen spanning tree $T$. Using techniques of Naddef and Pulleyblank [@naddefpulleyblank], Mömke and Svensson 