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This bound is best possible; there are infinitely many subcubic and cubic graphs whose minimum TSP walks have lengths $\\frac{5n+n_2}{4}-1$ and $\\frac{5n}{4} - 2$ respectively. We characterize the extremal subcubic examples meeting this bound. We also give a quadratic-time combinatorial algorithm for finding such a TSP walk. 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Wigal, Xingxing Yu, Youngho Yoo","submitted_at":"2021-12-12T16:59:46Z","abstract_excerpt":"We prove that every simple 2-connected subcubic graph on $n$ vertices with $n_2$ vertices of degree 2 has a TSP walk of length at most $\\frac{5n+n_2}{4}-1$, confirming a conjecture of Dvo\\v{r}\\'ak, Kr\\'al', and Mohar. This bound is best possible; there are infinitely many subcubic and cubic graphs whose minimum TSP walks have lengths $\\frac{5n+n_2}{4}-1$ and $\\frac{5n}{4} - 2$ respectively. We characterize the extremal subcubic examples meeting this bound. We also give a quadratic-time combinatorial algorithm for finding such a TSP walk. 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