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We prove new results for approximating the graphic TSP and some relatedproblems. We obtain polynomial-time algorithms with improved approximationguarantees.  For the graphic TSP itself, we improve the approximation ratio to 7/5. For ageneralization, the connected-$T$-join problem, we obtain the first nontrivialapproximation algorithm, with ratio 3/2. This contains the graphic$s$-$t$-path-TSP as a special case. Our improved approximation guarantee forfinding a smallest 2-edge-connected spanning subgraph is 4/3.  The key new ingredient of all our algorithms is a special kind ofear-decomposition optimized using forest representations of hypergraphs. Thesame methods also provide the lower bounds (arising from LP relaxations) thatwe use to deduce the approximation ratios.

Shorter Tours by Nicer Ears: 7/5-approximation for graphic TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs