A note on the directed genus of <em>K</em><sub><em>n</em>, <em>n</em>, <em>n</em></sub> and <em>K</em><sub><em>n</em></sub>

Authors

  • Rong-Xia Hao

DOI:

https://doi.org/10.26493/1855-3974.911.3b4

Keywords:

Digraph, complete tripartite graph, directed genus, surfaces

Abstract

It is proved that a complete graph Kn can have an orientation whose minimum directed genus is ⌈112(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 12(n - 1)(n - 2).

Author Biography

Rong-Xia Hao

Department of Mathematics, Beijing Jiaotong University,  Beijing 100044, P.R. China

Published

2017-10-24

Issue

Section

Articles