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arXiv · 2610.40540

A DG algebra structure for the edge ideal of any split graph

David Bronshvayg·Rachel Diethorn·Mario Stinson-Maas·Reed Wang
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Abstract

We construct an explicit DG algebra structure on the minimal free resolution of the quotient of a polynomial ring by the edge ideal of any split graph (that is, a graph whose vertex set is a disjoint union of a clique and an independent set). The algebra structure is based on a simple combinatorial notion, which we call the fixing edge of a pair of edges, that directly captures the structure of the underlying graph. Our construction involves an explicit description of the minimal free resolution of the edge ideal of such a graph, including formulas for both the Betti numbers and the differentials.

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David Bronshvayg, Rachel Diethorn, Mario Stinson-Maas, Reed Wang. 2026-10-29. A DG algebra structure for the edge ideal of any split graph. https://arxiv.org/abs/2610.40540

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