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

Authors:
Fedor V. Fomin;Sang-il Oum;Dimitrios M. Thilikos
Affiliations:
Department of Informatics, University of Bergen, N-5020 Bergen, Norway;Department of Mathematical Sciences, KAIST, Daejeon, 305-701, Republic of Korea;Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, GR-157 84, Athens, Greece
Venue:
European Journal of Combinatorics
Year:
2010

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Abstract

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.