Regularity and h-polynomials of Binomial Edge Ideals
نویسندگان
چکیده
منابع مشابه
Regularity Bounds for Binomial Edge Ideals
We show that the Castelnuovo–Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.
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Let $X=left( begin{array}{llll} x_1 & ldots & x_{n-1}& x_n\ x_2& ldots & x_n & x_{n+1} end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...
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We prove two recent conjectures on some upper bounds for the Castelnuovo-Mumford regularity of the binomial edge ideals of some different classes of graphs. We prove the conjecture of Matsuda and Murai for chordal graphs. We also prove the conjecture due to the authors for a class of chordal graphs. We determine the regularity of the binomial edge ideal of the join of graphs in terms of the reg...
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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...
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ژورنال
عنوان ژورنال: Acta Mathematica Vietnamica
سال: 2021
ISSN: 0251-4184,2315-4144
DOI: 10.1007/s40306-021-00416-3