Graphic Multi-Path TSP has a 2-approximation and LP integrality gap at most 2; Graphic Ordered TSP has a 1.791-approximation.
Worst-case analysis of a new heuristic for the travelling salesman problem
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Approximating Graphic Multi-Path TSP and Graphic Ordered TSP
Graphic Multi-Path TSP has a 2-approximation and LP integrality gap at most 2; Graphic Ordered TSP has a 1.791-approximation.