Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals

Jiawen Shan, Zexin Wang

For a bipartite graph $G$ and an integer $t\ge 2$, let $\NM_t(G)$ be its $t$-non-matching complex. We prove that adding an edge while preserving bipartiteness induces an injection…