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arXiv · 1712.10167

Simple cubic graphs with no short traveling salesman tour

Robert Lukoťka·Ján Mazák
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Abstract

Let $tsp(G)$ denote the length of a shortest travelling salesman tour in a graph $G$. We prove that for any $\varepsilon>0$, there exists a simple $2$-connected planar cubic graph $G_1$ such that $tsp(G_1)\ge (1.25-\varepsilon)\cdot|V(G_1)|$, a simple $2$-connected bipartite cubic graph $G_2$ such that $tsp(G_2)\ge (1.2-\varepsilon)\cdot|V(G_2)|$, and a simple $3$-connected cubic graph $G_3$ such that $tsp(G_3)\ge (1.125-\varepsilon)\cdot|V(G_3)|$.

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Robert Lukoťka, Ján Mazák. 2017-12-29. Simple cubic graphs with no short traveling salesman tour. https://arxiv.org/abs/1712.10167

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