We prove that the degeneracy of graphs in a hereditary class defined by a finite set S of forbidden induced subgraphs is bounded if and only if S includes a complete graph, a complete bipartite graph and a forest.
@article{arxiv.2206.09252,
title = {A dichotomy for graphs of bounded degeneracy},
author = {A. Atminas and V. Lozin},
journal= {arXiv preprint arXiv:2206.09252},
year = {2022}
}