Proof of the KalaiMeshulam conjecture
Abstract
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 $f_G= \pm 2$. 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 $f_G\le 1$. We prove this conjecture.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1810.00065
 Bibcode:
 2018arXiv181000065C
 Keywords:

 Mathematics  Combinatorics