Geodesic
A note on the directed genus of K_n,n,n and K_n
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 375-385.

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It is proved that a complete graph Kn can have an orientation whose minimum directed genus is ⌈1⁄12(n - 3)(n - 4)⌉ if and only if n ≡ 3, 7 (mod 12). This answers a question of Bonnington et al. by using a method different from current graphs. It is also proved that a complete symmetric tripartite graph Kn, n, n has an orientation whose minimum directed genus is 1⁄2(n - 1)(n - 2).
DOI : 10.26493/1855-3974.911.3b4
Keywords: Digraph, complete tripartite graph, directed genus, surfaces 
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Rong-Xia Hao. A note on the directed genus of K_n,n,n and K_n. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 375-385. doi : 10.26493/1855-3974.911.3b4. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.911.3b4/

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