Proof of the Kalai-Meshulam conjecture - Chudnovsky, M; Scott, A; Seymour, P; Spirkl, S (Springer, 2020)
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.