The authors prove preservation of linear quotients under vertex duplication and expansion, exhibit a new infinite family of gapfree CDCC graphs whose edge ideal powers have linear quotients, and reduce a conjecture about all powers to checking finitely many powers.
Banerjee, The regularity of powers of edge ideals, J
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Gapfree graphs and powers of edge ideals with linear quotients
The authors prove preservation of linear quotients under vertex duplication and expansion, exhibit a new infinite family of gapfree CDCC graphs whose edge ideal powers have linear quotients, and reduce a conjecture about all powers to checking finitely many powers.