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Edge Elimination and Weighted Graph Classes

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Graph-Theoretic Concepts in Computer Science (WG 2020)

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Abstract

Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light edges. This naturally leads to a generalization of the concept of a graph class to the weighted case by requiring that all level graphs belong to the class. We examine some types of monotonicity of graph classes, such as sandwich monotonicity, to construct edge elimination schemes of edge-weighted graphs. This leads to linear-time recognition algorithms of weighted graphs for which all level graphs are split, threshold, or chain graphs.

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Acknowledgements

The authors would like to thank Ulrik Brandes, Caroline Brosse, Christophe Crespelle, and Petr Golovach for their valuable discussions.

This research was funded in part by German Academic Exchange Service and the Slovenian Research Agency (BI-DE/17-19-18 and BI-DE/19-20-007), and by the Slovenian Research Agency (I0-0035, research programs P1-0285, P1-0383, P1-0404, research projects J1-1692, J1-9110, J1-9187, N1-0102, and N1-0160, and a Young Researchers Grant).

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Authors and Affiliations

  1. Brandenburg University of Technology, Cottbus, Germany

    Jesse Beisegel, Ekkehard Köhler, Robert Scheffler & Martin Strehler

  2. FAMNIT, University of Primorska, Koper, Slovenia

    Nina Chiarelli, Matjaž Krnc, Martin Milanič & Nevena Pivač

  3. IAM, University of Primorska, Koper, Slovenia

    Nina Chiarelli, Martin Milanič & Nevena Pivač

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  1. Jesse Beisegel
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Correspondence to Robert Scheffler .

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  1. University of Leeds, Leeds, UK

    Isolde Adler

  2. University of Leeds, Leeds, UK

    Haiko Müller

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Beisegel, J. et al. (2020). Edge Elimination and Weighted Graph Classes. In: Adler, I., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2020. Lecture Notes in Computer Science(), vol 12301. Springer, Cham. https://doi.org/10.1007/978-3-030-60440-0_11

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  • DOI: https://doi.org/10.1007/978-3-030-60440-0_11

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