Regularity of Powers of Edge Ideals of Some Graphs
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DOI: 10.1007/s40306-017-0204-5
Abstract: Let Cn~$\tilde {C_{n}}$ be the graph by adding an ear to Cn and I=I(Cn~)$I=I(\tilde {C_{n}})$ be its edge ideal. In this paper, we prove that reg(Is)=2s+⌊n+13⌋−1$\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1$ for all s ≥ 1.… read more here.
Keywords: frac rfloor; powers edge; regularity; lfloor frac ... See more keywords
ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS
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DOI: 10.1017/nmj.2020.27
Abstract: Abstract Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality… read more here.
Keywords: edge ideals; symbolic powers; powers edge; ideals graphs ... See more keywords
Powers of edge ideals with linear resolutions
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DOI: 10.1080/00927872.2018.1430810
Abstract: ABSTRACT We show that if G is a gap-free and diamond-free graph, then I(G)s has a linear minimal free resolution for every s≥2. read more here.
Keywords: ideals linear; powers edge; linear resolutions; edge ideals ... See more keywords
Associated primes of powers of edge ideals and ear decompositions of graphs
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DOI: 10.1090/tran/7662
Abstract: In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between… read more here.
Keywords: ear decompositions; powers edge; associated primes; ideals ear ... See more keywords
The powers of unmixed bipartite edge ideals
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DOI: 10.1142/s0219498819502098
Abstract: In this paper, we study the depth and the Castelnuovo–Mumford regularity of the powers of edge ideals which are unmixed and whose underlying graphs are bipartite. In particular, we prove that the depth of the… read more here.
Keywords: edge ideals; regularity; unmixed bipartite; powers edge ... See more keywords
Invariants of the symbolic powers of edge ideals
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DOI: 10.1142/s0219498820501844
Abstract: Let [Formula: see text] be a graph and [Formula: see text] be its edge ideal. When [Formula: see text] is the clique sum of two different length odd cycles joined at single vertex then we… read more here.
Keywords: powers edge; invariants symbolic; see text; formula see ... See more keywords