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

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.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Fedor V. Fomin, Sang-il Oum, Dimitrios M. Thilikos
• Keywords: EJC 2007, EJC 2010, Kr-minor Free Graphs, Topological Minor, Tree-width