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- W2419558051 abstract "Hartsfield and Ringel proved that a complete graph $K_n$ has an orientable quadrangular embedding if $nequiv 5 pmod 8$, and has a nonorientable quadrangular embedding if $n ge 9$ and $nequiv 1 pmod 4$. We complete the characterization of complete graphs admitting quadrangular embeddings by showing that $K_n$ has an orientable quadrilateral embedding if $n equiv 0 pmod 8$, and has a nonorientable quadrilateral embedding if $n equiv 0 pmod 4$. We also determine the order of minimal quadrangulations for some surfaces where the corresponding graphs are not complete." @default.
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- W2419558051 date "2016-06-03" @default.
- W2419558051 modified "2023-09-27" @default.
- W2419558051 title "Quadrangular embeddings of complete graphs" @default.
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