Regularity of two classes of Cohen-Macaulay binomial edge ideals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909303252713472 |
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| author | Bhardwaj, Om Prakash Saha, Kamalesh |
| author_facet | Bhardwaj, Om Prakash Saha, Kamalesh |
| contents | Some recent investigations indicate that for the classification of Cohen-Macaulay binomial edge ideals, it suffices to consider biconnected graphs with some whiskers attached (in short, `block with whiskers'). This paper provides explicit combinatorial formulae for the Castelnuovo-Mumford regularity of two specific classes of Cohen-Macaulay binomial edge ideals: (i) chain of cycles with whiskers and (ii) $r$-regular $r$-connected block with whiskers. For the first type, we introduce a new invariant of graphs in terms of the number of blocks in certain induced block graphs, and this invariant may help determine the regularity of other classes of binomial edge ideals. For the second type, we present the formula as a linear function of $r$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_01639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity of two classes of Cohen-Macaulay binomial edge ideals Bhardwaj, Om Prakash Saha, Kamalesh Commutative Algebra Combinatorics 13D02, 13H10, 13F65, 05E40, 05C25 Some recent investigations indicate that for the classification of Cohen-Macaulay binomial edge ideals, it suffices to consider biconnected graphs with some whiskers attached (in short, `block with whiskers'). This paper provides explicit combinatorial formulae for the Castelnuovo-Mumford regularity of two specific classes of Cohen-Macaulay binomial edge ideals: (i) chain of cycles with whiskers and (ii) $r$-regular $r$-connected block with whiskers. For the first type, we introduce a new invariant of graphs in terms of the number of blocks in certain induced block graphs, and this invariant may help determine the regularity of other classes of binomial edge ideals. For the second type, we present the formula as a linear function of $r$. |
| title | Regularity of two classes of Cohen-Macaulay binomial edge ideals |
| topic | Commutative Algebra Combinatorics 13D02, 13H10, 13F65, 05E40, 05C25 |
| url | https://arxiv.org/abs/2409.01639 |