Simple cubic graphs with no short traveling salesman tour

12/29/2017

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by   Robert Lukoťka, et al.

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