Kratsch, D. and Müller, H. (2009) On a property of minimal triangulations. Discrete Mathematics, 309 (6). 1724 -1729 . ISSN 0012-365X
Abstract
A graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal (chordal) triangulation of G is H-free. We show that a graph H satisfies property MT if and only if H is edgeless, H is connected and is an induced subgraph of P5, or H has two connected components and is an induced subgraph of 2P3.
This completes the results of Parra and Scheffler, who have shown that MT holds for H=Pk, the path on k vertices, if and only if k5 [A. Parra, P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics 79 (1997) 171–188], and of Meister, who proved that MT holds for ℓP2, ℓ copies of a P2, if and only if ℓ2 [D. Meister, A complete characterisation of minimal triangulations of 2K2-free graphs, Discrete Mathematics 306 (2006) 3327–3333].
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright © 2008 Elsevier B.V. This is an author produced version of a paper published in 'Discrete Mathematics'. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Chordal graph; Minimal triangulation; Minimal separator |
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) |
Depositing User: | Mrs Yasmin Aziz |
Date Deposited: | 18 Nov 2008 12:05 |
Last Modified: | 18 Jun 2015 17:26 |
Published Version: | http://dx.doi.org/10.1016/j.disc.2008.01.048 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.disc.2008.01.048 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:4918 |