Improved approximations for cubic bipartite and cubic TSP

摘要

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 $$5/4n-2$$ 5 / 4 n - 2 . For 2-connected cubic graphs, we show that the techniques of M?mke and Svensson can be combined with the techniques of Correa, Larré and Soto, to obtain a tour of length at most $$(4/3-1/8754)n$$ ( 4 / 3 - 1 / 8754 ) n .