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arXiv · 2503.13337

The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs

Trung Chau·Nursel Erey·Aryaman Maithani
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Abstract

Every monomial ideal $I$ has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that $I$ is Scarf if its Scarf complex is also its minimal free resolution. In this paper, we fully characterize all pairs $(G,n)$ of a graph $G$ and an integer $n$ such that the squarefree power $I(G)^{[n]}$ or the symbolic power $I(G)^{(n)}$ of the edge ideal $I(G)$ is Scarf. We also determine all graphs $G$ such that its cover ideal $J(G)$ is Scarf, with an explicit description when $G$ is either chordal or bipartite.

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Trung Chau, Nursel Erey, Aryaman Maithani. 2025-03-17. The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs. https://doi.org/10.1080/00927872.2025.2544296

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