报告题目： The Betti Number of the Independence Complex of Ternary Graphs

报 告 人：  吴河辉

报告人所在单位： 上海数学中心/复旦大学

报告日期： 2020-12-30 星期三

报告时间： 9:00-10:00

报告地点： 腾讯会议 ID：341 423 760， 密码:  24680

报告摘要： Given a graph $G$, the independence complex $I(G)$ is the simplicial complex whose faces are the independent sets of $V(G)$. Let $b_i$ denote the $i$-th reduced Betti number of $I(G)$, and let $b(G)$ denote the sum of $b_i(G)$'s. A graph is ternary if it does not contain induced cycles with length divisible by three. G. Kalai and K. Meshulam conjectured that $b(G)=2$ and $b(H)\in \{0,1\}$ for every induced subgraph $H$ of $G$ if and only if $G$ is a cycle with length divisible by three. We prove this conjecture. This extends a recent results proved by Chudnovsky, Scott, Seymour and Spirkl that for any ternary graph $G$, the number of independent sets with even cardinality and the independent sets with odd cardinality differ by at most 1.
This is joint work with a graduate student Wentao Zhang in Fudan University.