# Proof of the Kalai-Meshulam conjecture

@article{Chudnovsky2018ProofOT,
title={Proof of the Kalai-Meshulam conjecture},
author={M. Chudnovsky and Alex D. Scott and Paul D. Seymour and Sophie Theresa Spirkl},
journal={Israel Journal of Mathematics},
year={2018},
pages={1-23}
}
Let G be a graph, and let f G be the sum of (−1) ∣ A ∣ , over all stable sets A. If G is a cycle with length divisible by three, then f G = ±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 ∣ f G ∣ ≤ 1. We prove this conjecture.
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