In this paper, we investigate how local rules enforced at every node can influence the topology of a network. More precisely, we establish several results on the diameter of trees as a function of the number of nodes, as listed below. These results have important consequences on the landscape of locally checkable labelings (LCL) on \emph{unbounded} degree graphs, a case in which our lack of knowledge is in striking contrast with that of \emph{bounded degree graphs}, that has been intensively studied recently. [See paper for full abstract.]
@article{arxiv.2409.01305,
title = {How local constraints influence network diameter and applications to LCL generalizations},
author = {Nicolas Bousquet and Laurent Feuilloley and Théo Pierron},
journal= {arXiv preprint arXiv:2409.01305},
year = {2024}
}