Regularity and $h$-Polynomials of Edge Ideals
نویسندگان
چکیده
منابع مشابه
Regularity of second power of edge ideals
Let G be a graph with edge ideal I(G). Benerjee and Nevo proved that for every graph G, the inequality reg(I(G)2)≤reg(I(G))+2 holds. We provide an alternative proof for this result.
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A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...
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We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of invariants of the directed graph. For some classes of unmixed edge ideals, we show that the arithmetic rank of the ideal equals projective dimension of its quotient.
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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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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8247