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3d graph and hamilton cycle

Source: 2018 Korea Winter Mop Practice Test #8

February 25, 2018
combinatoricsgraph theory

Problem Statement

Graph GG is defined in 3d space. It has ee edges and every vertex are connected if the distance between them is 1.1. Given that there exists the Hamilton cycle, prove that for e>1,e>1, we have min⁡d(v)≤1+2(e2)0.4.\min d(v)\le 1+2\left(\frac{e}{2}\right)^{0.4}.
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