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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bronshvayg2026algebra,
  title = {{A DG algebra structure for the edge ideal of any split graph}},
  author = {David Bronshvayg and Rachel Diethorn and Mario Stinson-Maas and Reed Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40540},
  eprint = {2610.40540},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40540},
}
RIS
TY  - UNPB
TI  - A DG algebra structure for the edge ideal of any split graph
AU  - David Bronshvayg
AU  - Rachel Diethorn
AU  - Mario Stinson-Maas
AU  - Reed Wang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40540
UR  - https://arxiv.org/abs/2610.40540
AB  - 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.
ER  -