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Cheeger’s cut, maxcut and the spectral theory of 1-Laplacian on graphs

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Abstract

This is primarily an expository paper surveying up-to-date known results on the spectral theory of 1-Laplacian on graphs and its applications to the Cheeger cut, maxcut and multi-cut problems. The structure of eigenspace, nodal domains, multiplicities of eigenvalues, and algorithms for graph cuts are collected.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11371038, 11471025, 11421101 and 61121002).

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    KungChing Chang, SiHong Shao & Dong Zhang

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  1. KungChing Chang
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  2. SiHong Shao
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  3. Dong Zhang
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Correspondence to KungChing Chang.

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In honor of Professor CHENG MinDe

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Chang, K., Shao, S. & Zhang, D. Cheeger’s cut, maxcut and the spectral theory of 1-Laplacian on graphs. Sci. China Math. 60, 1963–1980 (2017). https://doi.org/10.1007/s11425-017-9096-6

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  • DOI: https://doi.org/10.1007/s11425-017-9096-6

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