Jinha Kim (김진하), On a conjecture by Kalai and Meshulam – the Betti number of the independence complex of ternary graphs

Given a graph G=(V,E), the independence complex of G is the abstract simplicial complex I(G) on V whose faces are the independent sets of G. A graph is ternary if it does not contain an induced cycle of length divisible by three. Kalai and Meshulam conjectured that if G is ternary then the sum of the Betti numbers of I(G) is either 0 or 1. In this talk, I will introduce a result by Zhang and Wu, which proves the Kalai-Meshulam conjecture.