da Silva, MVG and Vušković, K (2013) Decomposition of even-hole-free graphs with star cutsets and 2-joins. Journal of Combinatorial Theory. Series B, 103. 144 - 183. ISSN 0095-8956
Abstract
In this paper we consider the class of simple graphs defined by excluding, as induced subgraphs, even holes (i.e. chordless cycles of even length). These graphs are known as even-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, that uses star cutsets and 2-joins. This is a significant strengthening of the only other previously known decomposition of even-hole-free graphs, by Conforti, Cornuéjols, Kapoor and Vušković, that uses 2-joins and star, double star and triple star cutsets. It is also analogous to the decomposition of Berge (i.e. perfect) graphs with skew cutsets, 2-joins and their complements, by Chudnovsky, Robertson, Seymour and Thomas. The similarity between even-hole-free graphs and Berge graphs is higher than the similarity between even-hole-free graphs and simply odd-hole-free graphs, since excluding a 4-hole, automatically excludes all antiholes of length at least 6. In a graph that does not contain a 4-hole, a skew cutset reduces to a star cutset, and a 2-join in the complement implies a star cutset, so in a way it was expected that even-hole-free graphs can be decomposed with just the star cutsets and 2-joins. A consequence of this decomposition theorem is a recognition algorithm for even-hole-free graphs that is significantly faster than the previously known ones.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2012 Elsevier Inc. All rights reserved. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Combinatorial Theory. Series B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Combinatorial Theory. Series B,103, (2013)DOI 10.1016/j.jctb.2012.10.001 |
Keywords: | Even-hole-free graphics; star cutsets; 2-joins; recognition algorithm; decomposition |
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) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 May 2014 10:41 |
Last Modified: | 16 Nov 2016 11:51 |
Published Version: | http://dx.doi.org/10.1016/j.jctb.2012.10.001 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jctb.2012.10.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:78770 |