The Weisfeiler-Leman dimension of distance-hereditary graphs
Combinatorics
2020-05-26 v1 Computational Complexity
Discrete Mathematics
Abstract
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 . The previously best known upper bound for the dimension was .
Cite
@article{arxiv.2005.11766,
title = {The Weisfeiler-Leman dimension of distance-hereditary graphs},
author = {Alexander L. Gavrilyuk and Roman Nedela and Ilia Ponomarenko},
journal= {arXiv preprint arXiv:2005.11766},
year = {2020}
}