Graphs of small rank-width are pivot-minors of graphs of small tree-width

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We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors of trees and bipartite graphs of linear rank-width at most 1 are precisely pivot-minors of paths.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2014-05
Language
English
Article Type
Article
Citation

DISCRETE APPLIED MATHEMATICS, v.168, pp.108 - 118

ISSN
0166-218X
DOI
10.1016/j.dam.2013.01.007
URI
http://hdl.handle.net/10203/188969
Appears in Collection
MA-Journal Papers(저널논문)
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