Finding torus obstructions/graph theory and algorithms for chemistry

项目1：寻找环面障碍物-环面是一个形状像甜甜圈的表面。环面的一个拓扑障碍是一个最小度为3的图G，它不能嵌入到环面上，但对于所有的边e，G-e嵌入到环面上。一个小序障碍物有一个额外的属性，即对于所有的边e，G合同e嵌入环面。到目前为止，我们已经发现了249，227个拓扑障碍和17，354个次要障碍。我们未来研究的目标是使用独立计算来检查以前的结果，开发更好的计算工具，以便可以扩展搜索，搜索已知障碍物中的模式，以便它们可以更简洁地表达，生成并证明关于完整障碍物集的结构，并使用所获得的见解来开发用于环面嵌入的实用算法。

Project 1: Finding the Torus Obstructions- A torus is a surface shaped like a doughnut. A topological obstruction for the torus is a graph G with minimum degree three that is not embeddable on the torus but for all edges e, G-e embeds on the torus. A minor order obstruction has the additional property that for all edges e, G contract e embeds on the torus. To date, we have found 249,227 topological obstructions and 17,354 minor order obstructions. The aims of our future research are to check the previous results using independent computations, to develop better computational tools so that the search can be extended, to search for patterns in the known obstructions so that they can expressed more succinctly, to generate and prove conjectures regarding the complete set of obstructions, and to use the insights gained for developing practical algorithms for torus embedding.