Rank-width and tree-width of H-minor-free graphs

@article{Fomin2010RankwidthAT,
  title={Rank-width and tree-width of H-minor-free graphs},
  author={Fedor V. Fomin and Sang-il Oum and Dimitrios M. Thilikos},
  journal={Eur. J. Comb.},
  year={2010},
  volume={31},
  pages={1617-1628}
}
We prove that for any fixed r ≥ 2, the tree-width of graphs not containing Kr 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 Kr-minor free graphs and graphs of bounded genus. 
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