论文标题
引入边缘地图
Introducing edge-biregular maps
论文作者
论文摘要
我们介绍了图地图的替代边色的概念，并研究了此类地图的高度对称示例。 $（k，l）$类型的边缘射线图作为特定索引的平滑普通标，两个子组的$ t_ {k，l} $，描述常规平面$（k，l）$ tessellations的完整三角形组。可以通过四个参与来生成由此产生的染色自动形态组。当通常的四个发电机不是不同的参与时，我们将探索特殊情况，并将这些地图与完全常规的地图相关联。当辅助表面具有非负的欧拉特征时，我们对边缘射线图进行了分类，而当染色的自动形态组是二面体同构时，则在任意表面上的边缘线图。
We introduce the concept of alternate-edge-colourings for maps, and study highly symmetric examples of such maps. Edge-biregular maps of type $(k,l)$ occur as smooth normal quotients of a particular index two subgroup of $T_{k,l}$, the full triangle group describing regular plane $(k,l)$-tessellations. The resulting colour-preserving automorphism groups can be generated by four involutions. We explore special cases when the usual four generators are not distinct involutions, with constructions relating these maps to fully regular maps. We classify edge-biregular maps when the supporting surface has non-negative Euler characteristic, and edge-biregular maps on arbitrary surfaces when the colour-preserving automorphism group is isomorphic to a dihedral group.
