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Graph Stabilization: A Survey

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Combinatorial Optimization and Graph Algorithms

Abstract

Graph stabilization has raised a family of network design problems that has received considerable attention recently. Stable graphs are those graphs for which the matching game has non-empty core. In the optimization terminology, they are graphs for which the fractional matching linear program has an integral optimum solution. Graph stabilization involves minimally modifying a given graph to make it stable. In this survey, we outline recent developments in graph stabilization and highlight some open problems.

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Acknowledgements

I would like to thank my collaborators in [10, 12] and the authors of [2, 27] for sharing their insights and results at various conference venues. Thanks also to Chandra Chekuri, Britta Peis and Corinna Gottschalk for helpful suggestions on previous drafts of the article.

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  1. University of Illinois, Urbana-Champaign, IL, USA

    Karthekeyan Chandrasekaran

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  1. Karthekeyan Chandrasekaran
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Correspondence to Karthekeyan Chandrasekaran .

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  1. National Institute of Informatics , Tokyo, Japan

    Takuro Fukunaga

  2. National Institute of Informatics , Tokyo, Japan

    Ken-ichi Kawarabayashi

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Chandrasekaran, K. (2017). Graph Stabilization: A Survey. In: Fukunaga, T., Kawarabayashi, Ki. (eds) Combinatorial Optimization and Graph Algorithms. Springer, Singapore. https://doi.org/10.1007/978-981-10-6147-9_2

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  • DOI: https://doi.org/10.1007/978-981-10-6147-9_2

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