Abstract
Let I be the t-path ideal of Ln , the line graph with n-vertices. It is shown that Is has a linear resolution for some s ≥ 1 (or equivalently for all s ≥ 1 ) if and only if Is has linear quotients for some s ≥ 1 (or equivalently for all s ≥ 1 ) if and only if t ≤ n ≤ 2 t . In addition, we present an explicit formula for the regularity of Is for all s ≥ 1 . It turns out it is linear in s from the very beginning.
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