Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6872257 | Discrete Applied Mathematics | 2014 | 11 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
O-joung Kwon, Sang-il Oum,