Proof of the Kalai-Meshulam conjecture
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Authors
Chudnovsky, Maria
Scott, Alex
Seymour, Paul
Spirkl, Sophie
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Springer Nature
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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This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s11856-020-2034-8