Settling the genus of the $n$-prism

Abstract

In a 1977 paper, Ringel conjectured a formula for the genus of the $n$-prism $K_n\times K_2$ and verified its correctness for about five-sixths of all values $n$. We complete this calculation by showing that, with the exception of $n=9$, Ringel's conjecture is true for $n\equiv 5,9(\mathrm{mod}12)$.

14 pages, 7 figures; accepted to the European Journal of Combinatorics

References in corpus (2)

• Surface realization with the intersection edge functional
• Face distributions of embeddings of complete graphs