We prove that if G is a gap-free and chair-free simple graph,then the regularity of the edge ideal of G is no more than 3.If G is a gap-free and P4-free graph,then it is a chair-free graph;furthermore,the complement o...We prove that if G is a gap-free and chair-free simple graph,then the regularity of the edge ideal of G is no more than 3.If G is a gap-free and P4-free graph,then it is a chair-free graph;furthermore,the complement of G is chordal,and thus the regularity of G is 2.展开更多
We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge.These formulas axe functions in the weig...We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge.These formulas axe functions in the weight of the vertices,and the numbers of edges and cycles.Some examples show that these formulas are related to direction selection and the assumption that w(x)≥2 for any vertex x cannot be dropped.展开更多
In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomia...In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph.We also identify a certain subclass attaining the upper bound.展开更多
We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipart...We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipartite and fan graphs.In addition,we compute the Hilbert-Poincare series of the binomial edge ideals of some Cohen-Macaulaybipartitegraphs.展开更多
基金Research supported by the Natural Science Foundation of Shanghai(No.19ZR1424100)the National Natural Science Foundation of China(No.11971338).
文摘We prove that if G is a gap-free and chair-free simple graph,then the regularity of the edge ideal of G is no more than 3.If G is a gap-free and P4-free graph,then it is a chair-free graph;furthermore,the complement of G is chordal,and thus the regularity of G is 2.
基金supported by the National Natural Science Foundation of China(No.11271275)the Foundation of the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge.These formulas axe functions in the weight of the vertices,and the numbers of edges and cycles.Some examples show that these formulas are related to direction selection and the assumption that w(x)≥2 for any vertex x cannot be dropped.
文摘In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph.We also identify a certain subclass attaining the upper bound.
基金The first author was supported by the“National Group for Algebraic and Geometric Structures,and Their Applications”(GNSAGA-INdAM).
文摘We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipartite and fan graphs.In addition,we compute the Hilbert-Poincare series of the binomial edge ideals of some Cohen-Macaulaybipartitegraphs.
