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Edge Contraction and Forbidden Induced Subgraphs

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Graphs and Combinatorial Optimization: from Theory to Applications (CTW 2023)

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Abstract

Given a family of graphs \(\mathcal {H}\), a graph G is \(\mathcal {H}\)-free if any subset of V(G) does not induce a subgraph of G that is isomorphic to any graph in \(\mathcal {H}\). We present sufficient and necessary conditions for a graph G such that G/e is \(\mathcal {H}\)-free for any edge e in E(G). Thereafter, we use these conditions to characterize \(2K_{2}\)-free, \(C_{4}\)-free, \(C_{5}\)-free, and split graphs.

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Acknowledgements

The research presented here is funded by the European Social Fund (ESF).

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Authors and Affiliations

  1. KIT university, Karlsruhe, Germany

    Hany Ibrahim

  2. University of Applied Sciences Mittweida, Mittweida, Germany

    Peter Tittmann

Authors
  1. Hany Ibrahim
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  2. Peter Tittmann
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Correspondence to Hany Ibrahim .

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Editors and Affiliations

  1. Fakultät für Wirtschafts- und Organisationswissenschaften, Universität der Bundeswehr München, Munich, Germany

    Andreas Brieden

  2. Fakultät für Informatik, Universität der Bundeswehr München, Munich, Germany

    Stefan Pickl

  3. Fakultät für Informatik, Universität der Bundeswehr München, Munich, Germany

    Markus Siegle

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Ibrahim, H., Tittmann, P. (2024). Edge Contraction and Forbidden Induced Subgraphs. In: Brieden, A., Pickl, S., Siegle, M. (eds) Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023. AIRO Springer Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-031-46826-1_2

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