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Seunghun Lee (이승훈), Leray numbers of complexes of graphs with bounded matching number
Seunghun Lee (이승훈), Leray numbers of complexes of graphs with bounded matching number
Given a graph $G$ on the vertex set $V$, the non-matching complex of $G$, $\mathsf{NM}_k(G)$, is the family of subgraphs $G' \subset G$ whose matching number $\nu(G')$ is strictly less than $k$. As an attempt to generalize the result by Linusson, Shareshian and Welker on the homotopy types of $\mathsf{NM}_k(K_n)$ and $\mathsf{NM}_k(K_{r,s})$ to arbitrary graphs …