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- W1840693205 abstract "We survey basic properties and bounds for $q$-equivelar and $d$-covered triangulations of closed surfaces. Included in the survey is a list of the known sources for $q$-equivelar and $d$-covered triangulations. We identify all orientable and non-orientable surfaces $M$ of Euler characteristic $0>chi(M)geq -230$ which admit non-neighborly $q$-equivelar triangulations with equality in the upper bound $qleqBigllfloortfrac{1}{2}(5+sqrt{49-24chi (M)})Biglrfloor$. These examples give rise to $d$-covered triangulations with equality in the upper bound $dleq2Bigllfloortfrac{1}{2}(5+sqrt{49-24chi (M)})Biglrfloor$. A generalization of Ringel's cyclic $7{rm mod}12$ series of neighborly orientable triangulations to a two-parameter family of cyclic orientable triangulations $R_{k,n}$, $kgeq 0$, $ngeq 7+12k$, is the main result of this paper. In particular, the two infinite subseries $R_{k,7+12k+1}$ and $R_{k,7+12k+2}$, $kgeq 1$, provide non-neighborly examples with equality for the upper bound for $q$ as well as derived examples with equality for the upper bound for $d$." @default.
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- W1840693205 date "2010-01-15" @default.
- W1840693205 modified "2023-09-25" @default.
- W1840693205 title "Equivelar and d-Covered Triangulations of Surfaces. I" @default.
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