Kratsch, D. and Müller, H. (2009) On a property of minimal triangulations. Discrete Mathematics, 309 (6). 1724 -1729 . ISSN 0012-365X
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].
|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|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)|
|Depositing User:||Mrs Yasmin Aziz|
|Date Deposited:||18 Nov 2008 12:05|
|Last Modified:||18 Jun 2015 17:26|