The total Betti number of the independence complex of ternary graphs

  • Wentao Zhang

    Fudan University, Shanghai, China
  • Hehui Wu

    Fudan University, Shanghai, China
The total Betti number of the independence complex of ternary graphs cover

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Abstract

Given a graph , the independence complex is the simplicial complex whose faces are the independent sets of . Let denote the -th reduced Betti number of , and let denote the sum of the ’s. A graph is ternary if it does not contain induced cycles with length divisible by 3. Kalai and Meshulam conjectured that whenever is ternary. We prove this conjecture. This extends a recent result proved by Chudnovsky, Scott, Seymour and Spirkl that for any ternary graph , the number of independent sets with even cardinality and the number of independent sets with odd cardinality differ by at most 1.

Cite this article

Wentao Zhang, Hehui Wu, The total Betti number of the independence complex of ternary graphs. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1378