Improved approximations for cubic bipartite and cubic TSP

Abstract

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 M¨omke 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.