AI 中文总结
研究关于顶点和面度满足特定条件的连通平面图，通过Hurwitz存在性问题的结果推导相关结论，并给出对应Belyi函数的描述。
AI 中文摘要
我们表明，关于顶点和面度满足规定均匀性条件且至多有两个例外的连通平面图的各种已知和新结果，可从关于有理函数分支模式可实现性的Hurwitz存在性问题的近期结果推导得出。我们的方法还给出了与此类图对应的Belyi函数的描述。
英文摘要
We show that a variety of known and new results concerning connected plane graphs whose vertex and face degrees satisfy prescribed uniformity conditions with at most two exceptions can be deduced from recent results on the Hurwitz existence problem regarding the realizability of branch patterns of rational functions. Our method also yields a description of the Belyi functions corresponding to such graphs.
