论文标题
距离距离距离的Weisfeiler-Lean尺寸
The Weisfeiler-Leman dimension of distance-hereditary graphs
论文作者
论文摘要
如果每个连接的诱导子图中的距离函数与图本身相同，则据说图形是距离的。我们证明，如果其中一个是远距离的，则普通的Weisfeiler-Leman算法正确测试了任意两个图的同构；更确切地说，有限距离距离的weisfeiler-Lean尺寸等于$ 2 $。以前最著名的尺寸上限为$ 7 $。
A graph is said to be distance-hereditary if the distance function in every connected induced subgraph is the same as in the graph itself. We prove that the ordinary Weisfeiler-Leman algorithm correctly tests the isomorphism of any two graphs if one of them is distance-hereditary; more precisely, the Weisfeiler-Leman dimension of the class of finite distance-hereditary graphs is equal to $2$. The previously best known upper bound for the dimension was $7$.
