For even n we prove that the genus of the complete tripartite graph Kn,n,1 is ⌈(n−1)(n−2)/4⌉. 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.
@article{arxiv.1612.07888,
title = {On the genus of the complete tripartite graph $K_{n,n,1}$},
author = {Valentas Kurauskas},
journal= {arXiv preprint arXiv:1612.07888},
year = {2016}
}