Improved approximations for cubic bipartite and cubic TSP

We show improved approximation guarantees for the traveling salesman problem on cubic bipartite graphs and cubic graphs. For connected cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi 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 Momke and Svensson can be combined with the techniques of Correa, Larre and Soto, to obtain a tour of length at most \((4/3-1/8754)n\).