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

## Tuesday, December 22, 2020 @ 4:30 PM - 5:30 PM KST

Room B232,
IBS (기초과학연구원)

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.