Worst-case comparison of valid inequalities for the TSP
Mathematical Programming: Series A and B
SIAM Journal on Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
On The Approximability Of The Traveling Salesman Problem
Combinatorica
TSP on cubic and subcubic graphs
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Spanning closed walks and TSP in 3-connected planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A proof of the Boyd-Carr conjecture
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improving christofides' algorithm for the s-t path TSP
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the integrality gap of the subtour LP for the 1,2-TSP
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
An improved upper bound for the TSP in cubic 3-edge-connected graphs
Operations Research Letters
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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.