Binomial edge ideals of bipartite graphs
- Bolognini, Davide Département de Mathématiques, Université de Fribourg, Switzerland
- Macchia, Antonio Dipartimento di Matematica, Università degli Studi di Bari “Aldo Moro”, Bari, Italy
- Strazzanti, Francesco Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Spain
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01.05.2018
Published in:
- European Journal of Combinatorics. - 2018, vol. 70, p. 1–25
English
Binomial edge ideals are a noteworthy class of binomial ideals that can be associated with graphs, generalizing the ideals of 2-minors. For bipartite graphs we prove the converse of Hartshorne’s Connectedness Theorem, according to which if an ideal is Cohen–Macaulay, then its dual graph is connected. This allows us to classify Cohen–Macaulay binomial edge ideals of bipartite graphs, giving an explicit and recursive construction in graph-theoretical terms. This result represents a binomial analogue of the celebrated characterization of (monomial) edge ideals of bipartite graphs due to Herzog and Hibi (2005). Herzog J., Hibi T. Distributive lattices, bipartite graphs and Alexander duality J. Algebraic Combin., 22 (2005), pp. 289-302
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 309505
- DOI 10.1016/j.ejc.2017.11.004
- Persistent URL
- https://folia.unifr.ch/unifr/documents/306699
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