Graphs of Small Rank-width are Pivot-minors of Graphs of Small Tree-width
In: Discrete Applied Math. 168(May 11, 2014), pp. 108-118; (2012) S. 108-118
Online
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Zugriff:
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.
Comment: 16 pages, 7 figures
| Titel: |
Graphs of Small Rank-width are Pivot-minors of Graphs of Small Tree-width
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| Autor/in / Beteiligte Person: | Kwon, O-joung ; Oum, Sang-il |
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| Quelle: | Discrete Applied Math. 168(May 11, 2014), pp. 108-118; (2012) S. 108-118 |
| Veröffentlichung: | 2012 |
| Medientyp: | report |
| DOI: | 10.1016/j.dam.2013.01.007 |
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