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arXiv · 2503.21008

Density of linearity index in the interval of matching numbers

Nursel Erey·Takayuki Hibi
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Abstract

Given integers $2 \leq p \leq c \leq q$, 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 $I(G)$ of $G$ has linear quotients for each $c \leq k \leq q$ and is not linearly related for each $1 \leq k < c$, where $\nu_1(G)$ is the induced matching number of $G$ and $\nu(G)$ is the matching number of $G$.

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Nursel Erey, Takayuki Hibi. 2025-03-26. Density of linearity index in the interval of matching numbers. https://arxiv.org/abs/2503.21008

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