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We show improved approximation guarantees for the traveling salesman problemon cubic graphs, and cubic bipartite graphs. For cubic bipartite graphs with nnodes, we improve on recent results of Karp and Ravi (2014) by giving a simple"local improvement" algorithm that finds a tour of length at most 5/4 n - 2.For 2-connected cubic graphs, we show that the techniques of Moemke andSvensson (2011) can be combined with the techniques of Correa, Larre and Soto(2012), to obtain a tour of length at most (4/3-1/8754)n.

Improved Approximations for Cubic and Cubic Bipartite TSP