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The regularity of binomial edge ideals of graphs | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 7، دوره 1، شماره 2، آذر 2020، صفحه 217-221 اصل مقاله (276.11 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2020.16433.1024 | ||
| نویسندگان | ||
| Sara Saeedi Madani* ؛ Dariush Kiani | ||
| Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic),Tehran, Iran | ||
| چکیده | ||
| In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal. | ||
| کلیدواژهها | ||
| Binomial edge ideal؛ Castelnuovo-Mumford regularity؛ Free cut edge | ||
| مراجع | ||
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[6] D. Kiani, S. Saeedi Madani, Some Cohen-Macaulay and unmixed binomial edge ideals, Comm. Algebra. 43 (2015) 5434-5453.
[7] D. Kiani, S. Saeedi Madani, The Castelnuovo-Mumford regularity of binomial edge ideals, J. Combin. Theory Ser. A. 139 (2016) 80-86.
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[9] F. Mohammadi, L. Sharifan, Hilbert function of binomial edge ideals, Comm. Algebra 42 (2014) 688-703.
[10] S. Saeedi Madani, D. Kiani, Binomial edge ideals of graphs, Electron. J. Combin. 19(2) (2012) ] P44.
[11] P. Schenzel, S. Zafar, Algebraic properties of the binomial edge ideal of a complete bipartite graph, An. St. Univ. Ovidius Constanta, Ser. Mat. 22(2) (2014) 217-237.
[12] S. Zafar, On approximately Cohen-Macaulay binomial edge ideal, Bull. Math. Soc. Sci. Math. Roumanie, 55(103) (2012) 429-442.
[13] Z. Zahid, S. Zafar, On the Betti numbers of some classes of binomial edge ideals, Electron. J. Combin., 20(4) (2013) ] P37.
[14] S. Saeedi Madani, D. Kiani, On the binomial edge ideal of a pair of graphs, The Electronic Journal of Combinatorics. 20(1) (2013) ] P48.
[15] M. Rouzbahani Malayeri, S. Saeedi Madani, D. Kiani, Regularity of binomial edge ideals of chordal graphs, preprint. | ||
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