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Original Articles

Graphs and Ideals Generated by Some 2-Minors

Pages 905-917 | Received 14 Jul 2009, Published online: 16 Mar 2011

Keep up to date with the latest research on this topic with citation updates for this article.

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Marie Amalore Nambi & Neeraj Kumar. (2024) Regularity of powers of d-sequence (parity) binomial edge ideals of unicycle graphs. Communications in Algebra 52:6, pages 2598-2615.
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Hong Wang & Zhongming Tang. (2023) Depth of powers of binomial edge ideals of complete bipartite graphs. Communications in Algebra 51:6, pages 2472-2483.
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Ayah Almousa & Keller VandeBogert. (2022) Linear strands of initial ideals of determinantal facet ideals. Communications in Algebra 50:5, pages 2198-2214.
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A. V. Jayanthan & Arvind Kumar. (2019) Regularity of binomial edge ideals of Cohen-Macaulay bipartite graphs. Communications in Algebra 47:11, pages 4797-4805.
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Arvind Kumar & Rajib Sarkar. (2019) Hilbert series of binomial edge ideals. Communications in Algebra 47:9, pages 3830-3841.
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Dariush Kiani & Sara Saeedi Madani. (2015) Some Cohen–Macaulay and Unmixed Binomial Edge Ideals. Communications in Algebra 43:12, pages 5434-5453.
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Leila Sharifan. (2015) Binomial Edge Ideals with Special Set of Associated Primes. Communications in Algebra 43:2, pages 503-520.
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Julia Porcino & Irena Swanson. (2015) 2 × 2 Permanental Ideals of Hypermatrices. Communications in Algebra 43:1, pages 84-101.
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Fatemeh Mohammadi & Leila Sharifan. (2014) Hilbert Function of Binomial Edge Ideals. Communications in Algebra 42:2, pages 688-703.
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Asia Rauf & Giancarlo Rinaldo. (2014) Construction of Cohen–Macaulay Binomial Edge Ideals. Communications in Algebra 42:1, pages 238-252.
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Masahiro Ohtani. (2013) Binomial Edge Ideals of Complete Multipartite Graphs. Communications in Algebra 41:10, pages 3858-3867.
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Viviana Ene & Ayesha Asloob Qureshi. (2013) Ideals Generated by Diagonal 2-Minors. Communications in Algebra 41:8, pages 3058-3066.
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Articles from other publishers (71)

Rupam Karmakar, Rajib Sarkar & Aditya Subramaniam. (2024) Algebraic properties of binomial edge ideals of Levi graphs associated with curve arrangements. Journal of Pure and Applied Algebra 228:9, pages 107665.
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Nadia Taghipour, Shamila Bayati & Farhad Rahmati. (2023) Comparison of symbolic and ordinary powers of parity binomial edge ideals. Monatshefte für Mathematik 203:3, pages 695-710.
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Davide Bolognini, Antonio Macchia, Giancarlo Rinaldo & Francesco Strazzanti. (2024) Cohen-Macaulay binomial edge ideals of small graphs. Journal of Algebra 638, pages 189-213.
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Lisa Seccia. (2023) Binomial Edge Ideals of Weakly Closed Graphs. International Mathematics Research Notices 2023:24, pages 22045-22068.
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Takayuki Hibi & Sara Saeedi Madani. (2023) Diameter and Connectivity of Finite Simple Graphs. Mediterranean Journal of Mathematics 20:6.
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Giancarlo Rinaldo & Rajib Sarkar. (2023) Level and pseudo-Gorenstein binomial edge ideals. Journal of Algebra 632, pages 363-383.
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Irena Peeva. (2023) Closed binomial edge ideals. Journal für die reine und angewandte Mathematik (Crelles Journal) 0:0.
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Delio Jaramillo-Velez & Lisa Seccia. (2023) Connected domination in graphs and v-numbers of binomial edge ideals. Collectanea Mathematica.
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Alessandro De Stefani, Jonathan Montaño & Luis Núñez-Betancourt. (2022) Frobenius methods in combinatorics. São Paulo Journal of Mathematical Sciences 17:1, pages 387-429.
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Alberto Lerda, Carla Mascia, Giancarlo Rinaldo & Francesco Romeo. (2022) $$(S_2)$$-condition and Cohen–Macaulay binomial edge ideals. Journal of Algebraic Combinatorics 57:2, pages 589-615.
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I. Jahani, Sh. Bayati & F. Rahmati. (2022) On the Equality of Symbolic and Ordinary Powers of Binomial Edge Ideals. Bulletin of the Brazilian Mathematical Society, New Series 54:1.
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Yi-Huang Shen & Guangjun Zhu. (2022) Regularity of powers of (parity) binomial edge ideals. Journal of Algebraic Combinatorics 57:1, pages 75-100.
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Bruno Benedetti, Lisa Seccia & Matteo Varbaro. (2022) Hamiltonian paths, unit-interval complexes, and determinantal facet ideals. Advances in Applied Mathematics 141, pages 102407.
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Dariush Kiani, Sara Saeedi Madani & Saeed Tafazolian. (2022) Hankel Edge Ideals of Trees and (Semi-)Hamiltonian Graphs. Bulletin of the Malaysian Mathematical Sciences Society 45:5, pages 2493-2507.
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Viviana Ene, Giancarlo Rinaldo & Naoki Terai. (2022) Sequentially Cohen–Macaulay binomial edge ideals of closed graphs. Research in the Mathematical Sciences 9:3.
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Aldo Conca, Emanuela De Negri & Elisa Gorla. (2022) Radical Generic Initial Ideals. Vietnam Journal of Mathematics 50:3, pages 807-827.
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VIVIANA ENE, GIANCARLO RINALDO & NAOKI TERAI. (2021) POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES. Nagoya Mathematical Journal 246, pages 233-255.
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Davide Bolognini, Antonio Macchia, Francesco Strazzanti & Volkmar Welker. (2022) Powers of monomial ideals with characteristic-dependent Betti numbers. Research in the Mathematical Sciences 9:2.
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Davide Bolognini, Antonio Macchia & Francesco Strazzanti. (2021) Cohen–Macaulay binomial edge ideals and accessible graphs. Journal of Algebraic Combinatorics 55:4, pages 1139-1170.
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M. Rouzbahani Malayeri, S. Saeedi Madani & D. Kiani. (2022) On the depth of binomial edge ideals of graphs. Journal of Algebraic Combinatorics 55:3, pages 827-846.
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Arvind Kumar. (2022) Rees algebra and special fiber ring of binomial edge ideals of closed graphs. Illinois Journal of Mathematics 66:1.
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Takayuki Hibi & Kazunori Matsuda. (2021) Regularity and h-polynomials of Binomial Edge Ideals. Acta Mathematica Vietnamica 47:1, pages 369-374.
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Ayah Almousa & Keller VandeBogert. (2022) Determinantal facet ideals for smaller minors. Archiv der Mathematik 118:3, pages 247-256.
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Rajib Sarkar. (2021) Binomial edge ideals of unicyclic graphs. International Journal of Algebra and Computation 31:07, pages 1293-1318.
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René González‐Martínez. (2021) Gorenstein binomial edge ideals. Mathematische Nachrichten 294:10, pages 1889-1898.
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Trong Hoang Do & Thomas Kahle. (2020) Hilbert–Poincaré series of parity binomial edge ideals and permanental ideals of complete graphs. Collectanea Mathematica 72:3, pages 471-479.
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A.V. Jayanthan, Arvind Kumar & Rajib Sarkar. (2021) Almost complete intersection binomial edge ideals and their Rees algebras. Journal of Pure and Applied Algebra 225:6, pages 106628.
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Sara Saeedi Madani & Dariush Kiani. (2021) Induced matchings in strongly biconvex graphs and some algebraic applications. Mathematische Nachrichten 294:6, pages 1160-1174.
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Mohammad Rouzbahani Malayeri, Sara Saeedi Madani & Dariush Kiani. (2021) A proof for a conjecture on the regularity of binomial edge ideals. Journal of Combinatorial Theory, Series A 180, pages 105432.
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Mohammad Rouzbahani Malayeri, Sara Saeedi Madani & Dariush Kiani. (2020) Regularity of binomial edge ideals of chordal graphs. Collectanea Mathematica 72:2, pages 411-422.
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Arvind kumar. (2020) Binomial edge ideals and bounds for their regularity. Journal of Algebraic Combinatorics 53:3, pages 729-742.
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Mohammad Rouzbahani Malayeri, Sara Saeedi Madani & Dariush Kiani. (2021) Binomial edge ideals of small depth. Journal of Algebra 572, pages 231-244.
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Arvind Kumar. (2021) Lovász–Saks–Schrijver ideals and parity binomial edge ideals of graphs. European Journal of Combinatorics 93, pages 103274.
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Arvind Kumar. (2020) Binomial edge ideals of generalized block graphs. International Journal of Algebra and Computation 30:08, pages 1537-1554.
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A.V. Jayanthan, Arvind Kumar & Rajib Sarkar. (2020) Regularity of powers of quadratic sequences with applications to binomial ideals. Journal of Algebra 564, pages 98-118.
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Viviana Ene, Giancarlo Rinaldo & Naoki Terai. (2020) Licci binomial edge ideals. Journal of Combinatorial Theory, Series A 175, pages 105278.
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Arvind Kumar & Rajib Sarkar. (2020) Depth and extremal Betti number of binomial edge ideals. Mathematische Nachrichten 293:9, pages 1746-1761.
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Carla Mascia & Giancarlo Rinaldo. (2019) Krull dimension and regularity of binomial edge ideals of block graphs. Journal of Algebra and Its Applications 19:07, pages 2050133.
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Josep Àlvarez Montaner. (2019) Local cohomology of binomial edge ideals and their generic initial ideals. Collectanea Mathematica 71:2, pages 331-348.
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Arvind Kumar. (2020) Regularity bound of generalized binomial edge ideal of graphs. Journal of Algebra 546, pages 357-369.
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Do Trong Hoang. (2019) On the Betti numbers of edge ideals of skew Ferrers graphs. International Journal of Algebra and Computation 30:01, pages 125-139.
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Viviana Ene & Jürgen Herzog. 2020. Combinatorial Structures in Algebra and Geometry. Combinatorial Structures in Algebra and Geometry 43 50 .
A. V. Jayanthan, N. Narayanan & B. V. Raghavendra Rao. (2019) An upper bound for the regularity of binomial edge ideals of trees. Journal of Algebra and Its Applications 18:09, pages 1950170.
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A V Jayanthan, N Narayanan & B V Raghavendra Rao. (2019) Regularity of binomial edge ideals of certain block graphs. Proceedings - Mathematical Sciences 129:3.
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Giancarlo Rinaldo. (2019) Cohen–Macaulay binomial edge ideals of cactus graphs. Journal of Algebra and Its Applications 18:04, pages 1950072.
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Aldo Conca & Volkmar Welker. (2019) Lovász–Saks–Schrijver ideals and coordinate sections of determinantal varieties. Algebra & Number Theory 13:2, pages 455-484.
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Kazunori Matsuda. (2018) Weakly Closed Graphs and F -Purity of Binomial Edge Ideals . Algebra Colloquium 25:04, pages 567-578.
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Sara Saeedi Madani & Dariush Kiani. (2018) Binomial edge ideals of regularity 3. Journal of Algebra 515, pages 157-172.
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Davide Bolognini, Antonio Macchia & Francesco Strazzanti. (2018) Binomial edge ideals of bipartite graphs. European Journal of Combinatorics 70, pages 1-25.
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Jürgen Herzog, Takayuki Hibi & Hidefumi OhsugiJürgen Herzog, Takayuki Hibi & Hidefumi Ohsugi. 2018. Binomial Ideals. Binomial Ideals 171 238 .
Sara Saeedi Madani. 2018. Multigraded Algebra and Applications. Multigraded Algebra and Applications 83 94 .
Hernán de Alba & Do Trong Hoang. (2017) On the extremal Betti numbers of the binomial edge ideal of closed graphs. Mathematische Nachrichten 291:1, pages 28-40.
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Anargyros Katsabekis. (2017) Arithmetical rank of binomial ideals. Archiv der Mathematik 109:4, pages 323-334.
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Faryal Chaudhry & Ayesha Asloob Qureshi. (2017) Hankel ideals of 2-minors associated with pairs of proper intervals graphs. Journal of Algebra and Its Applications 16:04, pages 1750070.
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Jennifer Biermann, Augustine O'Keefe & Adam Van Tuyl. (2017) Bounds on the regularity of toric ideals of graphs. Advances in Applied Mathematics 85, pages 84-102.
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Jürgen Herzog, Dariush Kaini & Sara Saeedi Madani. (2017) The linear strand of determinantal facet ideals. Michigan Mathematical Journal 66:1.
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Irena Swanson & Eduardo Sáenz-de-Cabezón. 2017. Computations and Combinatorics in Commutative Algebra. Computations and Combinatorics in Commutative Algebra 41 75 .
Hamid Damadi & Farhad Rahmati. (2016) Smoothness in Binomial Edge Ideals. Mathematics 4:2, pages 37.
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Dariush Kiani & Sara Saeedi Madani. (2016) The Castelnuovo–Mumford regularity of binomial edge ideals. Journal of Combinatorial Theory, Series A 139, pages 80-86.
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David A. Cox & Andrew Erskine. (2016) On closed graphs, II. Involve, a Journal of Mathematics 9:2, pages 333-345.
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Viviana Ene, Jürgen Herzog & Takayuki Hibi. (2015) Linear flags and Koszul filtrations. Kyoto Journal of Mathematics 55:3.
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Rafael Villarreal. 2015. Monomial Algebras, Second Edition. Monomial Algebras, Second Edition 639 668 .
Viviana Ene & Andrei Zarojanu. (2015) On the regularity of binomial edge ideals. Mathematische Nachrichten 288:1, pages 19-24.
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Dariush Kiani & Sara Saeedi Madani. (2014) Binomial edge ideals with pure resolutions. Collectanea Mathematica 65:3, pages 331-340.
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Johannes Rauh & Nihat Ay. (2013) Robustness, canalyzing functions and systems design. Theory in Biosciences 133:2, pages 63-78.
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Viviana Ene, Jürgen Herzog, Takayuki Hibi & Ayesha Asloob Qureshi. (2016) The binomial edge ideal of a pair of graphs. Nagoya Mathematical Journal 213, pages 105-125.
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Viviana Ene, Jürgen Herzog & Takayuki Hibi. 2014. Bridging Algebra, Geometry, and Topology. Bridging Algebra, Geometry, and Topology 125 136 .
Irena Swanson & Amelia Taylor. (2013) Minimal primes of ideals arising from conditional independence statements. Journal of Algebra 392, pages 299-314.
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Johannes Rauh. (2013) Generalized binomial edge ideals. Advances in Applied Mathematics 50:3, pages 409-414.
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Viviana Ene, Jürgen Herzog & Takayuki Hibi. (2016) Cohen-Macaulay binomial edge ideals. Nagoya Mathematical Journal 204, pages 57-68.
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Jürgen Herzog, Takayuki Hibi, Freyja Hreinsdóttir, Thomas Kahle & Johannes Rauh. (2010) Binomial edge ideals and conditional independence statements. Advances in Applied Mathematics 45:3, pages 317-333.
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