Density of linearity index in the interval of matching numbers

Nursel Erey, Takayuki Hibi

Given integers $2\le p\le c\le q$, we construct a finite simple graph $G$ with ${\nu }_1(G)=p$ and $\nu (G)=q$ for which the squarefree power $I(G{)}^{[k]}$ of the edge ideal $I(G)…