Organized research on topological graph theory centered around re-embeddings ofgraphs

通过计算机实验，我们修正了已发表的环面上面板结构分类的错误，并发现了在亏格2的可定向闭曲面上重新嵌入不分解为初等部分的三角剖分的例子。作为重嵌入理论的应用，给出了闭曲面上图的两条独立边扩张为完全匹配的充分条件，并给出了具体曲面上禁止扩张的结构。我们还证明了闭曲面上可区别三角剖分个数的上界的存在性，并给出了射影平面和环面的最小上界。

By computer experiments, we fixed errors in the classification of panel structures on the torus already published, and found an example of re-embedding of a triangulation on the orientable closed surface of genus 2 that does not decompose into elementary parts. As applications of re-embedding theory, we gave a sufficient condition for two independent edges in a graph on a closed surface to extend to a perfect matching, and specified the structures on concrete surface forbidding such extension. We also showed the existence of an upper bound for the distinguishing numbers of triangulations on a closed surface and gave the least upper bounds for the projective plane and the torus.