Density of linearity index in the interval of matching numbers

Fuente: arXiv
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Main Authors: Erey, Nursel, Hibi, Takayuki
Format: Preprint
Published: 2025
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author Erey, Nursel
Hibi, Takayuki
author_facet Erey, Nursel
Hibi, Takayuki
contents Given integers $2 \leq p \leq c \leq q$, we construct a finite simple graph $G$ with $ν_1(G) = p$ and $ν(G) = q$ 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 $ν_1(G)$ is the induced matching number of $G$ and $ν(G)$ is the matching number of $G$.
format Preprint
id arxiv_https___arxiv_org_abs_2503_21008
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Density of linearity index in the interval of matching numbers
Erey, Nursel
Hibi, Takayuki
Commutative Algebra
Combinatorics
Given integers $2 \leq p \leq c \leq q$, we construct a finite simple graph $G$ with $ν_1(G) = p$ and $ν(G) = q$ 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 $ν_1(G)$ is the induced matching number of $G$ and $ν(G)$ is the matching number of $G$.
title Density of linearity index in the interval of matching numbers
topic Commutative Algebra
Combinatorics
url https://arxiv.org/abs/2503.21008