Koszul Binomial Edge Ideals
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915744611041280 |
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| author | LaClair, Adam Mastroeni, Matthew McCullough, Jason Peeva, Irena |
| author_facet | LaClair, Adam Mastroeni, Matthew McCullough, Jason Peeva, Irena |
| contents | As the binomial edge ideal of a graph is always generated by homogeneous quadratic polynomials corresponding to the edges of the graph, the question of when a binomial edge ideal defines a Koszul algebra has been studied by many authors ever since the class of ideals was first defined. Several partial results are known, including a characterization of those binomial edge ideals that possess a quadratic Gröbner basis. However, a complete characterization of the graphs determining Koszul binomial edge ideals has remained elusive. Inspired by our recent work characterizing when the graded Möbius algebras of graphic matroids are Koszul, we answer the question once and for all by proving that a graph defines a Koszul binomial edge ideal if and only if it is strongly chordal and claw-free. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Koszul Binomial Edge Ideals LaClair, Adam Mastroeni, Matthew McCullough, Jason Peeva, Irena Commutative Algebra Combinatorics Primary: 16S37, 05C75, Secondary: 13P10, 05E40, 05C25 As the binomial edge ideal of a graph is always generated by homogeneous quadratic polynomials corresponding to the edges of the graph, the question of when a binomial edge ideal defines a Koszul algebra has been studied by many authors ever since the class of ideals was first defined. Several partial results are known, including a characterization of those binomial edge ideals that possess a quadratic Gröbner basis. However, a complete characterization of the graphs determining Koszul binomial edge ideals has remained elusive. Inspired by our recent work characterizing when the graded Möbius algebras of graphic matroids are Koszul, we answer the question once and for all by proving that a graph defines a Koszul binomial edge ideal if and only if it is strongly chordal and claw-free. |
| title | Koszul Binomial Edge Ideals |
| topic | Commutative Algebra Combinatorics Primary: 16S37, 05C75, Secondary: 13P10, 05E40, 05C25 |
| url | https://arxiv.org/abs/2601.15243 |