Improved Approximations for Cubic Bipartite and Cubic TSP

  • Anke van Zuylen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)


We show improved approximation guarantees for the traveling salesman problem on cubic bipartite graphs and cubic graphs. For cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi [10] by giving a “local improvement” algorithm that finds a tour of length at most \(5/4n-2\). For 2-connected cubic graphs, we show that the techniques of Mömke and Svensson [11] can be combined with the techniques of Correa et al. [6], to obtain a tour of length at most \((4/3-1/8754)n\).


Traveling salesman problem Approximation algorithm Cubic bipartite graphs Cubic graphs Barnette’s conjecture 



The author would like to thank Marcin Mucha for careful reading and pointing out an omission in a previous version, Frans Schalekamp for helpful discussions, and an anonymous reviewer for suggesting the simplified proof for the result in Sect. 3 for cubic non-bipartite graphs. Other anonymous reviewers are acknowledged for helpful feedback on the presentation of the algorithm for bipartite cubic graphs.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsCollege of William & MaryWilliamsburgUSA

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