We prove an inequality involving the degeneracy, the cutwidth and the sparsity of graphs. It implies a quadratic lower bound on the cutwidth in terms of the degeneracy for all graphs and an improvement of it for clique-free graphs.
@article{arxiv.0907.5138,
title = {Cutwidth and degeneracy of graphs},
author = {Benoit Kloeckner},
journal= {arXiv preprint arXiv:0907.5138},
year = {2010}
}