The Weisfeiler-Leman Dimension of Distance-Hereditary Graphs

摘要

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 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.

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