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PreprintCC BY 4.0arXiv

Binomial edge ideals of bipartite complements of even cycles

  • Shahnawaz Ahmad Rather
  • S. Pirzada
  • M. Aijaz
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Abstract

Let Gn be the bipartite complement of the even cycle C2n, and let JGn be its binomial edge ideal. For n≥5, we study the interaction between the combinatorial structure of Gn and the algebraic invariants of SGn/JGn. Our main combinatorial ingredient is a classification of the subsets of V(Gn) having the cut point property, obtained through an analysis of disconnected induced subgraphs of Gn. We use this classification to describe the minimal primes and to study dimension and degree-theoretic invariants of JGn and SGn/JGn. We also study local Vasconcelos numbers, graded Betti numbers and the Hilbert series, and obtain information on projective dimension and depth. Finally, we analyze induced paths in Gn and derive corresponding bounds for the Castelnuovo--Mumford regularity.

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Cite

BibTeXRIS
BibTeX
@misc{rather2026binomial,
  title = {{Binomial edge ideals of bipartite complements of even cycles}},
  author = {Shahnawaz Ahmad Rather and S. Pirzada and M. Aijaz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32860},
  eprint = {2609.32860},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32860},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Binomial edge ideals of bipartite complements of even cycles
AU  - Shahnawaz Ahmad Rather
AU  - S. Pirzada
AU  - M. Aijaz
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32860
UR  - https://arxiv.org/abs/2609.32860
AB  - Let G_n be the bipartite complement of the even cycle C_2n, and let J_G_n be its binomial edge ideal. For n≥5, we study the interaction between the combinatorial structure of G_n and the algebraic invariants of S_G_n/J_G_n. Our main combinatorial ingredient is a classification of the subsets of V(G_n) having the cut point property, obtained through an analysis of disconnected induced subgraphs of G_n. We use this classification to describe the minimal primes and to study dimension and degree-theoretic invariants of J_G_n and S_G_n/J_G_n. We also study local Vasconcelos numbers, graded Betti numbers and the Hilbert series, and obtain information on projective dimension and depth. Finally, we analyze induced paths in G_n and derive corresponding bounds for the Castelnuovo--Mumford regularity.
ER  -