用BFS刻画无AT图

摘要：

一个星形三元组自由图是这样的图，对于每个独立的顶点三元组，任何两个顶点之间都没有路径避开第三个顶点。在Corneil和Stacho最近的一个结果中，这些图通过称为AT自由序的线性顶点排序来表征。在这里，我们使用的技术，从抽象凸几何，以改善这一结果，给出一个顶点的顺序表征具有更强的结构特性，从而解决了一个悬而未决的问题由Corneil和Stacho。这些排序是由运行在多项式时间的BFS的修改产生的。此外，我们给出了一个线性时间算法，它采用多个应用程序的（L）BFS计算AT-自由的订单在无爪AT-自由图和这些推广。

英文摘要：

An asteroidal triple free graph is a graph such that for every independent triple of vertices no path between any two avoids the third. In a recent result from Corneil and Stacho, these graphs were characterised through a linear vertex ordering called an AT-free order. Here, we use techniques from abstract convex geometry to improve on this result by giving a vertex order characterisation with stronger structural properties and thus resolve an open question by Corneil and Stacho. These orderings are generated by a modification of BFS which runs in polynomial time. Furthermore, we give a linear time algorithm which employs multiple applications of (L)BFS to compute AT-free orders in claw-free AT-free graphs and a generalisation of these.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。