Graphic TSP in 2-connected cubic graphs
نویسندگان
چکیده
We prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7 − 1, and that such a walk can be found in polynomial time. This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs. On the negative side, we show that there exist simple 2-connected cubic n-vertex graphs with no spanning closed walk of length less than 5n/4− 1.
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Graphic TSP in Cubic Graphs
We present a polynomial-time 9/7-approximation algorithm for the graphic TSP for cubic graphs, which improves the previously best approximation factor of 1.3 for 2-connected cubic graphs and drops the requirement of 2-connectivity at the same time. To design our algorithm, we prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7− 1, and ...
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