Density of linearity index in the interval of matching numbers
Abstract
Given integers 2 ≤ p ≤ c ≤ q, we construct a finite simple graph G with 1(G) = p and (G) = q for which the squarefree power I(G)[k] of the edge ideal I(G) of G has linear quotients for each c ≤ k ≤ q and is not linearly related for each 1 ≤ k < c, where 1(G) is the induced matching number of G and (G) is the matching number of G.
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