arXiv:1612.07888math.CO
On the genus of the complete tripartite graph $K_{n,n,1}$
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Abstract
For even $n$ we prove that the genus of the complete tripartite graph $K_{n,n,1}$ is $\lceil (n-1) (n-2)/4 \rceil$. This is the least number of bridges needed to build a complete $n$-way road interchange where changing lanes is not allowed. Both the theoretical result, and the surprising link to modelling road intersections are new.
Here, two very much related papers, albeit the title of the first one wouldn't tell you that: https://arxiv.org/abs/1612.07888 Kurauskas, Valentas - On the genus of the complete tripartite graph Kn,n,1 [2017] https://arxiv.org/abs/1801.03860 Kurauskas, Valentas; Šiurienė, Ugnė…
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