Diot, E, Radovanović, M, Trotignon, N et al. (1 more author) (2020) The (theta, wheel)-free graphs Part I: Only-prism and only-pyramid graphs. Journal of Combinatorial Theory. Series B, 143. pp. 123-147. ISSN 0095-8956
Abstract
Truemper configurations are four types of graphs (namely thetas, wheels, prisms and pyramids) that play an important role in the proof of several decomposition theorems for hereditary graph classes. In this paper, we prove two structure theorems: one for graphs with no thetas, wheels and prisms as induced subgraphs, and one for graphs with no thetas, wheels and pyramids as induced subgraphs. A consequence is a polynomial time recognition algorithms for these two classes. In Part II of this series we generalize these results to graphs with no thetas and wheels as induced subgraphs, and in Parts III and IV, using the obtained structure, we solve several optimization problems for these graphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (C) 2018 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Keywords: | Structure theorem; Decomposition; Truemper configuration; Recognition algorithm; Induced subgraph; Clique cutset; 2-Join |
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: | Symplectic Publications |
Date Deposited: | 19 Jan 2018 12:01 |
Last Modified: | 05 Aug 2020 09:53 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jctb.2017.12.004 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:93203 |