We 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. |

__Keywords__

Graph Embeddings, Directed Graphs

__Math Review Classification__

Primary 05C10

__Last Updated__

27/2/2002

__Length__

12

__Availability__

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