Rinaldo, Giancarlo Cohen-Macaulay binomial edge ideals of cactus graphs. (English) Zbl 1419.13042 J. Algebra Appl. 18, No. 4, Article ID 1950072, 18 p. (2019). In this paper under review, the author classifies the Cohen-Macaulay binomial edge ideals of cactus and bicyclic graphs. Reviewer: Amir Mafi (Sanandaj and Tehran) Cited in 11 Documents MSC: 13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes 05C40 Connectivity Keywords:binomial ideal; unmixed ideal; Cohen-Macaulay Software:CoCoA PDFBibTeX XMLCite \textit{G. Rinaldo}, J. Algebra Appl. 18, No. 4, Article ID 1950072, 18 p. (2019; Zbl 1419.13042) Full Text: DOI arXiv References: [1] Banerjee, A. and Nunez-Betancourt, L., Graph connectivity and binomial edge ideals, Proc. Amer. Math. Soc.145(2) (2017) 487-499. · Zbl 1356.13008 [2] Bolognini, D., Macchia, A. and Strazzanti, F., Binomial edge ideals of bipartite graphs, European J. Combin.70 (2018) 1-25. · Zbl 1384.05094 [3] CoCoATeam, CoCoA: A system for doing computations in commutative algebra, http://cocoa.dima.unige.it. [4] Ene, V., Herzog, J. and Hibi, T., Cohen-Macaulay binomial edge ideals, Nagoya Math. J.204 (2011) 57-68. · Zbl 1236.13011 [5] Harary, F., Graph Theory, (Addison-Wesley, 1972). · Zbl 0235.05105 [6] Herzog, J., Hibi, T., Hreinsdottir, F., Kahle, T. and Rauh, J., Binomial edge ideals and conditional independence statements, Adv. in Appl. Math.45 (2010) 317-333. · Zbl 1196.13018 [7] Kiani, D. and Madani, S. Saeedi, Some Cohen-Macaulay and unmixed binomial edge ideals, Comm. Algebra43 (2015) 5434-5453. · Zbl 1335.13008 [8] Ohtani, M., Graphs and ideals generated by some \(2\)-minors, Comm. Algebra39 (2011) 905-917. · Zbl 1225.13028 [9] Rauf, A. and Rinaldo, G., Construction of Cohen-Macaulay binomial edge ideals, Comm. Algebra42 (2014) 238-252. · Zbl 1293.13007 [10] Rinaldo, G., Cohen-Macaulay binomial edge ideals of small deviation, Bull. Math. Soc. Sci. Math. Roumanie56(104)(4) (2013) 497-503. · Zbl 1299.13026 [11] Villarreal, R. H., Cohen-Macaulay graphs, Manuscripta Math.66 (1990) 277-293. · Zbl 0737.13003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.