Vertex decomposability and regularity of very well-covered graphs
نویسندگان
چکیده
منابع مشابه
Sequentially Cohen-macaulay Bipartite Graphs: Vertex Decomposability and Regularity
Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen-Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the Castelnuovo-Mumford regularity of R/I(G) can be determined from the invariants of G.
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In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.
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Let G = (V,E) be a graph. If G is a König graph or if G is a graph without 3-cycles and 5-cycles, we prove that the following conditions are equivalent: ∆G is pure shellable, R/I∆ is Cohen-Macaulay, G is an unmixed vertex decomposable graph and G is well-covered with a perfect matching of König type e1, . . . , eg without 4-cycles with two ei’s. Furthermore, we study vertex decomposable and she...
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If sk denotes the number of stable sets of cardinality k in the graph G,
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in this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially cohen-macaulay.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2011
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2011.02.005