Ma'u, Sikimeti2009-08-282009-08-282002-02Department of Mathematics - Research Reports-478 (2002)1173-0889http://hdl.handle.net/2292/5150We consider embeddings of Eulerian digraphs that have in-arcs alternating with out-arcs in the rotation schemes at each vertex. We define the multicycle $C^{l,m}_n$ to be the digraph on the vertex set ${v_1,v_2,ldots,v_n}$, with arcs comprising $l$ copies of the cycle $(v_1,v_2,ldots,v_n)$ and $m$ copies of the cycle $(v_n,v_{n-1}, ldots, v_1)$. We consider maximal embeddings of multicycles and show that all except the bracelet digraphs $C^{1,1}_n$ are upper-embeddable. We find that some multicycles have the maximum possible genus range, being both upper-embeddable and planar, and some multicycles have a genus range of zero.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmTechnical ReportFields of Research::230000 Mathematical Sciences::230100 MathematicsThe author(s)