Proof of the Kalai-Meshulam conjecture
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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  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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Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl (2020). Proof of the Kalai-Meshulam conjecture. UWSpace. http://hdl.handle.net/10012/18516