Adler, I, Kante, MM and Kwon, O-J (2014) Linear Rank-Width of Distance-Hereditary Graphs. In: Kratsch, D and Todinca, I, (eds.) Graph-Theoretic Concepts in Computer Science. 40th International Workshop (WG 2014), 25-27 Jun 2014, Nouan-le-Fuzelier, France. Lecture Notes in Computer Science (8747). Springer , pp. 42-55. ISBN 978-3-319-12339-4
Abstract
We present a characterization of the linear rank-width of distance-hereditary graphs. Using the characterization, we show that the linear rank-width of every n-vertex distance-hereditary graph can be computed in time O(n²⋅log(n)), and a linear layout witnessing the linear rank-width can be computed with the same time complexity. For our characterization, we combine modifications of canonical split decompositions with an idea of [Megiddo, Hakimi, Garey, Johnson, Papadimitriou: The complexity of searching a graph. JACM 1988], used for computing the path-width of trees. We also provide a set of distance-hereditary graphs which contains the set of distance-hereditary vertex-minor obstructions for linear rank-width. The set given in [Jeong, Kwon, Oum: Excluded vertex-minors for graphs of linear rank-width at most k. STACS 2013: 221–232] is a subset of our obstruction set.
Metadata
Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | © 2014 Springer International Publishing Switzerland. This is an author produced version of a paper published in Lecture Notes in Computer Science. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-12340-0_4. Uploaded in accordance with the publisher's self-archiving policy. |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Oct 2016 08:58 |
Last Modified: | 16 Jan 2018 20:43 |
Published Version: | http://dx.doi.org/10.1007/978-3-319-12340-0_4 |
Status: | Published |
Publisher: | Springer |
Series Name: | Lecture Notes in Computer Science |
Identification Number: | 10.1007/978-3-319-12340-0_4 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:105529 |