Bounds For Invariants of Edge-Rings

By Isidoro Gitler, C. E. Valencia. 2005

50 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Regularity of Squarefree Monomial Ideals (2013, background): “t the smallest size of a vertex cover in Gis equal to the height of I(G). A graph Gis called unmixed if all minimal vertex cover of Ghas the same cardinality. For an unmixed graph G, it is known (cf. [24]) that 2htI(G) jX(G)j. A graph Gis called very well-covered (see [38]) if Gis unmixed, has no is”
Cohen-Macaulay edge ideal whose height is half of the number of vertices (2009, background): “For this ideal the following theorem [5] is known:”
Vertex decomposability and regularity of very well-covered graphs (2010, background): “In [5] it is shown that for a well-covered graph we have 2ht (I(G)) ≥ |V (G)|.”
Depths of Powers of the Edge Ideal of a Tree (2009, background): “Then depth R/I has been studied by various authors (see for example [8, 9, 15]).”
Edge ideals: algebraic and combinatorial properties (2010, background): “[46] If C is a d-uniform clutter and I = I(C), then e(R/I) ≤ dα0(C).”