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Journal articles on the topic 'Binomial edge ideals'

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Published: 11 March 2023

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1

Rauh, Johannes. "Generalized binomial edge ideals." Advances in Applied Mathematics 50, no. 3 (March 2013): 409–14. http://dx.doi.org/10.1016/j.aam.2012.08.009.

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2

Ene, Viviana, Giancarlo Rinaldo, and Naoki Terai. "Licci binomial edge ideals." Journal of Combinatorial Theory, Series A 175 (October 2020): 105278. http://dx.doi.org/10.1016/j.jcta.2020.105278.

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3

Kahle, Thomas, Camilo Sarmiento, and Tobias Windisch. "Parity binomial edge ideals." Journal of Algebraic Combinatorics 44, no. 1 (December 21, 2015): 99–117. http://dx.doi.org/10.1007/s10801-015-0657-3.

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4

Ene, Viviana, Jürgen Herzog, and Takayuki Hibi. "Cohen-Macaulay binomial edge ideals." Nagoya Mathematical Journal 204 (December 2011): 57–68. http://dx.doi.org/10.1215/00277630-1431831.

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5

Ene, Viviana, Jürgen Herzog, and Takayuki Hibi. "Cohen-Macaulay binomial edge ideals." Nagoya Mathematical Journal 204 (December 2011): 57–68. http://dx.doi.org/10.1017/s0027763000010394.

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6

Chaudhry, Faryal, Ahmet Dokuyucu, and Rida Irfan. "On the binomial edge ideals of block graphs." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (June 1, 2016): 149–58. http://dx.doi.org/10.1515/auom-2016-0033.

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Abstract We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph has the same depth as its initial ideal.
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7

Damadi, Hamid, and Farhad Rahmati. "Smoothness in Binomial Edge Ideals." Mathematics 4, no. 2 (June 1, 2016): 37. http://dx.doi.org/10.3390/math4020037.

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8

Matsuda, Kazunori, and Satoshi Murai. "Regularity bounds for binomial edge ideals." Journal of Commutative Algebra 5, no. 1 (March 2013): 141–49. http://dx.doi.org/10.1216/jca-2013-5-1-141.

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9

Mohammadi, Fatemeh, and Leila Sharifan. "Hilbert Function of Binomial Edge Ideals." Communications in Algebra 42, no. 2 (October 18, 2013): 688–703. http://dx.doi.org/10.1080/00927872.2012.721037.

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10

Kumar, Arvind, and Rajib Sarkar. "Hilbert series of binomial edge ideals." Communications in Algebra 47, no. 9 (March 26, 2019): 3830–41. http://dx.doi.org/10.1080/00927872.2019.1570241.

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11

Saeedi Madani, Sara, and Dariush Kiani. "Binomial edge ideals of regularity 3." Journal of Algebra 515 (December 2018): 157–72. http://dx.doi.org/10.1016/j.jalgebra.2018.08.027.

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12

Kiani, Dariush, and Sara Saeedi Madani. "Binomial edge ideals with pure resolutions." Collectanea Mathematica 65, no. 3 (March 12, 2014): 331–40. http://dx.doi.org/10.1007/s13348-014-0107-x.

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13

Banerjee, Arindam, and Luis Núñez-Betancourt. "Graph connectivity and binomial edge ideals." Proceedings of the American Mathematical Society 145, no. 2 (August 18, 2016): 487–99. http://dx.doi.org/10.1090/proc/13241.

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14

Bolognini, Davide, Antonio Macchia, and Francesco Strazzanti. "Binomial edge ideals of bipartite graphs." European Journal of Combinatorics 70 (May 2018): 1–25. http://dx.doi.org/10.1016/j.ejc.2017.11.004.

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15

Mascia, Carla, and Giancarlo Rinaldo. "Extremal Betti Numbers of Some Cohen–Macaulay Binomial Edge Ideals." Algebra Colloquium 28, no. 03 (July 26, 2021): 415–30. http://dx.doi.org/10.1142/s1005386721000328.

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We provide the regularity and the Cohen–Macaulay type of binomial edge ideals of Cohen–Macaulay cones, and we show the extremal Betti numbers of some classes of Cohen–Macaulay binomial edge ideals: Cohen–Macaulay bipartite and fan graphs. In addition, we compute the Hilbert–Poincaré series of the binomial edge ideals of some Cohen–Macaulay bipartite graphs.
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16

Ohtani, Masahiro. "Binomial Edge Ideals of Complete Multipartite Graphs." Communications in Algebra 41, no. 10 (October 3, 2013): 3858–67. http://dx.doi.org/10.1080/00927872.2012.680219.

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17

Rauf, Asia, and Giancarlo Rinaldo. "Construction of Cohen–Macaulay Binomial Edge Ideals." Communications in Algebra 42, no. 1 (October 18, 2013): 238–52. http://dx.doi.org/10.1080/00927872.2012.709569.

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18

Dokuyucu, Ahmet, Ajdin Halilovic, and Rida Irfan. "Gorenstein binomial edge ideals associated with scrolls." Communications in Algebra 45, no. 6 (October 7, 2016): 2602–12. http://dx.doi.org/10.1080/00927872.2016.1233219.

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19

Kumar, Arvind. "Binomial edge ideals of generalized block graphs." International Journal of Algebra and Computation 30, no. 08 (August 28, 2020): 1537–54. http://dx.doi.org/10.1142/s0218196720500526.

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We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo–Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by [Formula: see text], where [Formula: see text] is the number of minimal cut sets of the graph [Formula: see text] and obtain an improved upper bound for the regularity in terms of the number of maximal cliques and pendant vertices of [Formula: see text].
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20

Herzog, Jürgen, Takayuki Hibi, Freyja Hreinsdóttir, Thomas Kahle, and Johannes Rauh. "Binomial edge ideals and conditional independence statements." Advances in Applied Mathematics 45, no. 3 (September 2010): 317–33. http://dx.doi.org/10.1016/j.aam.2010.01.003.

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21

Ene, Viviana, and Andrei Zarojanu. "On the regularity of binomial edge ideals." Mathematische Nachrichten 288, no. 1 (April 25, 2014): 19–24. http://dx.doi.org/10.1002/mana.201300186.

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22

Àlvarez Montaner, Josep. "Local cohomology of binomial edge ideals and their generic initial ideals." Collectanea Mathematica 71, no. 2 (September 29, 2019): 331–48. http://dx.doi.org/10.1007/s13348-019-00268-z.

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23

Kumar, Arvind. "Lovász–Saks–Schrijver ideals and parity binomial edge ideals of graphs." European Journal of Combinatorics 93 (March 2021): 103274. http://dx.doi.org/10.1016/j.ejc.2020.103274.

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24

Ene, Viviana, Jürgen Herzog, Takayuki Hibi, and Ayesha Asloob Qureshi. "The binomial edge ideal of a pair of graphs." Nagoya Mathematical Journal 213 (March 2014): 105–25. http://dx.doi.org/10.1215/00277630-2389872.

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AbstractWe introduce a class of ideals generated by a set of 2-minors of an (m×n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.
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25

Ene, Viviana, Jürgen Herzog, Takayuki Hibi, and Ayesha Asloob Qureshi. "The binomial edge ideal of a pair of graphs." Nagoya Mathematical Journal 213 (March 2014): 105–25. http://dx.doi.org/10.1017/s0027763000026192.

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AbstractWe introduce a class of ideals generated by a set of 2-minors of an (m×n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.
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26

Kimura, Kyouko, and Naoki Terai. "Binomial arithmetical rank of edge ideals of forests." Proceedings of the American Mathematical Society 141, no. 6 (January 2, 2013): 1925–32. http://dx.doi.org/10.1090/s0002-9939-2013-11473-5.

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27

Rinaldo, Giancarlo. "Cohen–Macaulay binomial edge ideals of cactus graphs." Journal of Algebra and Its Applications 18, no. 04 (March 25, 2019): 1950072. http://dx.doi.org/10.1142/s0219498819500725.

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28

Kiani, Dariush, and Sara Saeedi Madani. "Some Cohen–Macaulay and Unmixed Binomial Edge Ideals." Communications in Algebra 43, no. 12 (August 24, 2015): 5434–53. http://dx.doi.org/10.1080/00927872.2014.952734.

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29

Baskoroputro, Herolistra, Viviana Ene, and Cristian Ion. "Koszul binomial edge ideals of pairs of graphs." Journal of Algebra 515 (December 2018): 344–59. http://dx.doi.org/10.1016/j.jalgebra.2018.08.029.

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30

Kiani, Dariush, and Sara Saeedi Madani. "The Castelnuovo–Mumford regularity of binomial edge ideals." Journal of Combinatorial Theory, Series A 139 (April 2016): 80–86. http://dx.doi.org/10.1016/j.jcta.2015.11.004.

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31

Mascia, Carla, and Giancarlo Rinaldo. "Krull dimension and regularity of binomial edge ideals of block graphs." Journal of Algebra and Its Applications 19, no. 07 (July 23, 2019): 2050133. http://dx.doi.org/10.1142/s0219498820501339.

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We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of block graphs by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present linear time algorithms to compute the Castelnuovo–Mumford regularity and the Krull dimension of binomial edge ideals of block graphs.
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32

Jayanthan, A. V., and Rajib Sarkar. "Bound for the Regularity of Binomial Edge Ideals of Cactus Graphs." Algebra Colloquium 29, no. 03 (July 26, 2022): 443–52. http://dx.doi.org/10.1142/s1005386722000347.

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In this article, we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique. As a consequence, we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph. We also identify a certain subclass attaining the upper bound.
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33

Sharifan, Leila. "Binomial Edge Ideals with Special Set of Associated Primes." Communications in Algebra 43, no. 2 (August 25, 2014): 503–20. http://dx.doi.org/10.1080/00927872.2014.918371.

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34

Kumar, Arvind, and Rajib Sarkar. "Depth and extremal Betti number of binomial edge ideals." Mathematische Nachrichten 293, no. 9 (July 7, 2020): 1746–61. http://dx.doi.org/10.1002/mana.201900150.

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35

Jayanthan, A. V., N. Narayanan, and B. V. Raghavendra Rao. "An upper bound for the regularity of binomial edge ideals of trees." Journal of Algebra and Its Applications 18, no. 09 (July 17, 2019): 1950170. http://dx.doi.org/10.1142/s0219498819501706.

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36

Matsuda, Kazunori. "Weakly Closed Graphs and F-Purity of Binomial Edge Ideals." Algebra Colloquium 25, no. 04 (December 2018): 567–78. http://dx.doi.org/10.1142/s1005386718000391.

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Herzog, Hibi, Hreindóttir et al. introduced the class of closed graphs, and they proved that the binomial edge ideal JG of a graph G has quadratic Gröbner bases if G is closed. In this paper, we introduce the class of weakly closed graphs as a generalization of the closed graph, and we prove that the quotient ring S/JG of the polynomial ring [Formula: see text] with K a field and [Formula: see text] is F-pure if G is weakly closed. This fact is a generalization of Ohtani’s theorem.
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37

Jayanthan, A. V., and Arvind Kumar. "Regularity of binomial edge ideals of Cohen-Macaulay bipartite graphs." Communications in Algebra 47, no. 11 (April 26, 2019): 4797–805. http://dx.doi.org/10.1080/00927872.2019.1596278.

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38

Jayanthan, A. V., Arvind Kumar, and Rajib Sarkar. "Almost complete intersection binomial edge ideals and their Rees algebras." Journal of Pure and Applied Algebra 225, no. 6 (June 2021): 106628. http://dx.doi.org/10.1016/j.jpaa.2020.106628.

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39

Lajmiri, Bahareh, Farhad Rahmati, and Mahdis Saeedi. "COHEN-MACAULAY BINOMIAL EDGE IDEALS OF SOME CLASSES OF GRAPHS." JP Journal of Algebra, Number Theory and Applications 42, no. 1 (April 11, 2019): 137–50. http://dx.doi.org/10.17654/nt042010137.

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40

Rouzbahani Malayeri, Mohammad, Sara Saeedi Madani, and Dariush Kiani. "A proof for a conjecture on the regularity of binomial edge ideals." Journal of Combinatorial Theory, Series A 180 (May 2021): 105432. http://dx.doi.org/10.1016/j.jcta.2021.105432.

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41

Hoang, Do Trong. "On the Betti numbers of edge ideals of skew Ferrers graphs." International Journal of Algebra and Computation 30, no. 01 (September 19, 2019): 125–39. http://dx.doi.org/10.1142/s021819671950067x.

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We prove that [Formula: see text] for any staircase skew Ferrers graph [Formula: see text], where [Formula: see text] and [Formula: see text]. As a consequence, Ene et al. conjecture is confirmed to hold true for the Betti numbers in the last column of the Betti table in a particular case. An explicit formula for the unique extremal Betti number of the binomial edge ideal of some closed graphs is also given.
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42

Schenzel, Peter, and Sohail Zafar. "Algebraic properties of the binomial edge ideal of a complete bipartite graph." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 2 (June 1, 2014): 217–38. http://dx.doi.org/10.2478/auom-2014-0043.

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AbstractLet JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is the ideal generated by the binomials xiyj − xjyi, 1 ≤ i < j≤ n, in the polynomial ring S = K[x1, . . . , xn, y1, . . . , yn] where {i, j} is an edge of G. We study the arithmetic properties of S/JG for G, the complete bipartite graph. In particular we compute dimensions, depths, Castelnuovo-Mumford regularities, Hilbert functions and multiplicities of them. As main results we give an explicit description of the modules of deficiencies, the duals of local cohomology modules, and prove the purity of the minimal free resolution of S/JG.
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43

Zafar, Sohail, and Zohaib Zahid. "Initial ideal of binomial edge ideal in degree 2." Novi Sad Journal of Mathematics 45, no. 2 (December 20, 2015): 187–99. http://dx.doi.org/10.30755/nsjom.2014.064.

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44

Kumar, Arvind. "Regularity bound of generalized binomial edge ideal of graphs." Journal of Algebra 546 (March 2020): 357–69. http://dx.doi.org/10.1016/j.jalgebra.2019.10.051.

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45

Matsuda, Kazunori, Hidefumi Ohsugi, and Kazuki Shibata. "Toric Rings and Ideals of Stable Set Polytopes." Mathematics 7, no. 7 (July 10, 2019): 613. http://dx.doi.org/10.3390/math7070613.

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In the present paper, we study the normality of the toric rings of stable set polytopes, generators of toric ideals of stable set polytopes, and their Gröbner bases via the notion of edge polytopes of finite nonsimple graphs and the results on their toric ideals. In particular, we give a criterion for the normality of the toric ring of the stable set polytope and a graph-theoretical characterization of the set of generators of the toric ideal of the stable set polytope for a graph of stability number two. As an application, we provide an infinite family of stable set polytopes whose toric ideal is generated by quadratic binomials and has no quadratic Gröbner bases.
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46

de Alba, Hernán, and Do Trong Hoang. "On the extremal Betti numbers of the binomial edge ideal of closed graphs." Mathematische Nachrichten 291, no. 1 (November 16, 2017): 28–40. http://dx.doi.org/10.1002/mana.201700292.

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47

González‐Martínez, René. "Gorenstein binomial edge ideals." Mathematische Nachrichten, September 2, 2021. http://dx.doi.org/10.1002/mana.201900251.

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48

Kiani, Dariush, and Sara Saeedi. "Binomial Edge Ideals of Graphs." Electronic Journal of Combinatorics 19, no. 2 (June 13, 2012). http://dx.doi.org/10.37236/2349.

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We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms. Finally, we give an upper bound for the Castelnuovo-Mumford regularity of the binomial edge ideal of a closed graph.
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49

Kahle, Thomas, and Jonas Krüsemann. "Binomial edge ideals of cographs." Revista de la Unión Matemática Argentina, August 17, 2022, 305–16. http://dx.doi.org/10.33044/revuma.2247.

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50

Seccia, Lisa. "Binomial Edge Ideals of Weakly Closed Graphs." International Mathematics Research Notices, December 19, 2022. http://dx.doi.org/10.1093/imrn/rnac346.

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Abstract Closed graphs have been characterized by Herzog et al. as the graphs whose binomial edge ideals have a quadratic Gröbner basis with respect to a diagonal term order. In this paper, we focus on a generalization of closed graphs, namely weakly closed graphs (or co-comparability graphs). Building on some results about Knutson ideals of generic matrices, we characterize weakly closed graphs as the only graphs whose binomial edge ideals are Knutson ideals for a certain polynomial $f$. In doing so, we re-prove Matsuda’s theorem about the F-purity of binomial edge ideals of weakly closed graphs in positive characteristic and we extend it to generalized binomial edge ideals. Furthermore, we give a characterization of weakly closed graphs in terms of the minimal primes of their binomial edge ideals and we characterize all minimal primes of Knutson ideals for this choice of $f$.
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