Adler, I, Le, NK, Muller, H et al. (3 more authors) (2017) On rank-width of even-hole-free graphs. Discrete Mathematics and Theoretical Computer Science, 19 (1). 25. ISSN 1462-7264
Abstract
We present a class of (diamond, even hole)-free graphs with no clique cutset that has unbounded rank-width. In general, even-hole-free graphs have unbounded rank-width, because chordal graphs are even-hole-free. A. A. da Silva, A. Silva and C. Linhares-Sales (2010) showed that planar even-hole-free graphs have bounded rank-width, and N. K. Le (2016) showed that even-hole-free graphs with no star cutset have bounded rank width. A natural question is to ask, whether even-hole-free graphs with no clique cutsets have bounded rank-width. Our result gives a negative answer. Hence we cannot apply the meta-theorem by Courcelle, Makowsky and Rotics, which would provide efficient algorithms for a large number of problems, including the maximum independent set problem, whose complexity remains open for (diamond, even hole)-free graphs.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 by the Author(s). Distributed under a Creative Commons Attribution 4.0 International License. | ||||
Keywords: | even-hole-free graph, (diamond, even hole)-free graph, clique cutset, clique-width, rank-width | ||||
Dates: |
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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) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 17 Jul 2017 11:21 | ||||
Last Modified: | 06 Sep 2019 14:51 | ||||
Published Version: | http://dmtcs.episciences.org/3827 | ||||
Status: | Published | ||||
Publisher: | Discrete Mathematics and Theoretical Computer Science | ||||
Identification Number: | https://doi.org/10.23638/DMTCS-19-1-24 |