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.

中文翻译：

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Kalai-Meshulam 猜想的证明

令 G 为图，令 f G 为 (−1) ∣ A ∣ 的和，在所有稳定集合 A 上。如果 G 是长度可被 3 整除的循环，则 f G = ±2。受拓扑考虑的启发，G. Kalai 和 R. Meshulam [8] 做出了以下猜想：如果图 G 的诱导圈的长度不能被 3 整除，则 ∣ f G ∣ ≤ 1。我们证明了这个猜想。