亏格4曲面上Hanani-Tutte定理的一个推广的反例
Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4
摘要：
在亏格$4$的可定向曲面上找到了亏格$5$的一个图及其绘图，其中每对独立边相交偶数次.这表明强Hanani-Tutte定理不能推广到亏格$4$的可定向曲面。作为一个基本步骤，在建设中，我们使用一个反例的统一Hanani-Tutte定理的环面上的扩展。
英文摘要：
We find a graph of genus $5$ and its drawing on the orientable surface of genus $4$ with every pair of independent edges crossing an even number of times. This shows that the strong Hanani-Tutte theorem cannot be extended to the orientable surface of genus $4$. As a base step in the construction we use a counterexample to an extension of the unified Hanani-Tutte theorem on the torus.
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