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Proof of the Kalai-Meshulam conjecture

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Abstract

Let G be a graph, and let fG be the sum of (−1)∣A∣, over all stable sets A. If G is a cycle with length divisible by three, then fG = ±2. Motivated by topological considerations, G. Kalai and R. Meshulam [8] made the conjecture that, if no induced cycle of a graph G has length divisible by three, then ∣fG∣ ≤ 1. We prove this conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544, USA

    Maria Chudnovsky, Paul Seymour & Sophie Spirkl

  2. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

    Alex Scott

Authors
  1. Maria Chudnovsky
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  2. Alex Scott
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  3. Paul Seymour
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  4. Sophie Spirkl
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Corresponding author

Correspondence to Paul Seymour.

Additional information

Supported by NSF Grant DMS-1763817. This material is based upon work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant number W911NF-16-1-0404.

Supported by a Leverhulme Trust Research Fellowship.

Supported by ONR grant N00014-14-1-0084 and NSF grant DMS-1265563.

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Chudnovsky, M., Scott, A., Seymour, P. et al. Proof of the Kalai-Meshulam conjecture. Isr. J. Math. 238, 639–661 (2020). https://doi.org/10.1007/s11856-020-2034-8

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  • DOI: https://doi.org/10.1007/s11856-020-2034-8

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