Vuskovic, K (2013) The world of hereditary graph classes viewed through Truemper configurations. In: Surveys in Combinatorics 2013. 24th British Combinatorial Conference, 30 Jun - 05 Jul 2013, Royal Holloway, University of London. Cambridge University Press , 265 - 325. ISBN 978-1-107-65195-1
Abstract
In 1982 Truemper gave a theorem that characterizes graphs whose edges can be labeled so that all chordless cycles have prescribed parities. The characterization states that this can be done for a graph G if and only if it can be done for all induced subgraphs of G that are of few speci c types, that we will call Truemper con gurations. Truemper was originally motivated by the problem of obtaining a co-NP characterization of bipartite graphs that are signable to be balanced (i.e. bipartite graphs whose node-node incidence matrices are balanceable matrices). The con gurations that Truemper identi ed in his theorem ended up playing a key role in understanding the structure of several seemingly diverse classes of objects, such as regular matroids, balanceable matrices and perfect graphs. In this survey we view all these classes, and more, through the excluded Truemper con gurations, focusing on the algorithmic consequences, trying to understand what structurally enables e cient recognition and optimization algorithms.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2013, Cambridge University Press. This is an author produced version of a paper published in Surveys in Combinatorics 2013. Uploaded with permission from the publisher. |
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: | 27 Jun 2014 09:09 |
Last Modified: | 19 Dec 2022 13:27 |
Published Version: | http://www.cambridge.org/gb/academic/subjects/math... |
Status: | Published |
Publisher: | Cambridge University Press |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79331 |