A note on the directed genus of Kn, n, n and Kn

Rong-Xia Hao

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).

Keywords


Digraph, complete tripartite graph, directed genus, surfaces

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

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications