Cantankerous maps and rotary embeddings of \(K_ n\)
A regular map is a 2-cell embedding of some graph on a closed surface such that the automorphism group of the embedding acts transitively on the flags, i.e., the triples consisting of a vertex, edge and face that are mutually incident. The author studies a class of non-orientable regular maps that contain an orientation-reversing cycle of length 2 and calls them cantankerous. He establishes various properties of cantankerous maps and shows that every regular map whose underlying graph is not simple is either cantankerous or is an appropriate branched covering over a regular map of a simple graph. Finally he applies the results to show that the complete graph of order greater than 6 (possibly with multiple edges of the same multiplicity) has no regular map. The same result (with multiplicity one) was established by \textit{L. D. James} [Ars Comb. 16-B, 57-72 (1983; Zbl 0539.05029)].
scientific article; zbMATH DE number 4125421