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Lower Bounds for Max-Cut via Semidefinite Programming

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LATIN 2020: Theoretical Informatics (LATIN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12118))

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Abstract

For a graph G, let f(G) denote the size of the maximum cut in G. The problem of estimating f(G) as a function of the number of vertices and edges of G has a long history and was extensively studied in the last fifty years. In this paper we propose an approach, based on semidefinite programming (SDP), to prove lower bounds on f(G). We use this approach to find large cuts in graphs with few triangles and in \(K_r\)-free graphs.

Alexandra Kolla was supported by NSF CAREER grant 1452923 as well as NSF AF grant 1814385.

Ray Li was supported by an NSF GRF grant DGE-1656518 and by NSF grant CCF-1814629.

Nitya Mani was supported in part by a Stanford Undergraduate Advising and Research Major Grant.

Luca Trevisan was supported by the NSF under grant CCF 181543 and his work on this project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 834861).

Benny Sudakov was supported in part by SNSF grant 200021_196965.

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Acknowledgements

The authors thank Jacob Fox and Matthew Kwan for helpful discussions and feedback. The authors thank Joshua Brakensiek for finding an error in an earlier draft of this paper. The authors thank Joshua Brakensiek and Yuval Wigderson for helpful feedback on an earlier draft of the paper.

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Authors and Affiliations

  1. Department of Computer Science, University of Colorado Boulder, Boulder, CO, 80302, USA

    Charles Carlson & Alexandra Kolla

  2. Department of Computer Science, Stanford University, Stanford, CA, 94305, USA

    Ray Li

  3. Department of Mathematics and Computer Science, Stanford University, Stanford, CA, 94305, USA

    Nitya Mani

  4. Department of Mathematics, ETH, 8092, Zurich, Switzerland

    Benny Sudakov

  5. Department of Decision Sciences, Bocconi University, Milan, Italy

    Luca Trevisan

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  1. Charles Carlson
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  2. Alexandra Kolla
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  3. Ray Li
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  4. Nitya Mani
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  5. Benny Sudakov
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  6. Luca Trevisan
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Corresponding author

Correspondence to Charles Carlson .

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Editors and Affiliations

  1. University of São Paulo, São Paulo, Brazil

    Yoshiharu Kohayakawa

  2. University of Campinas, Campinas, Brazil

    Flávio Keidi Miyazawa

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Carlson, C., Kolla, A., Li, R., Mani, N., Sudakov, B., Trevisan, L. (2020). Lower Bounds for Max-Cut via Semidefinite Programming. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_38

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  • DOI: https://doi.org/10.1007/978-3-030-61792-9_38

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