TSP Tours in Cubic Graphs: Beyond 4/3

After a sequence of improvements Boyd, Sitters, van der Ster, and Stougie proved that any 2-connected graph whose n vertices have degree 3, i.e., a cubic graph, has a Hamiltonian tour of length at most (4/3)n, establishing in particular that the integrality gap of the subtour LP is at most 4/3 for cubic graphs and matching the conjectured value of the famous 4/3 conjecture. In this paper we improve upon this result by designing an algorithm that finds a tour of length (4/3−1/61236)n, implying that cubic graphs are among the few interesting classes for which the integrality gap of the subtour LP is strictly less than 4/3.

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