We prove that for any fixed r>=2, the tree-width of graphs not containing K_r as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph classes such as K_r-minor free graphs and graphs of bounded genus.
@article{arxiv.0910.0079,
title = {Rank-width and Tree-width of H-minor-free Graphs},
author = {Fedor V. Fomin and Sang-il Oum and Dimitrios M. Thilikos},
journal= {arXiv preprint arXiv:0910.0079},
year = {2014}
}