Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes
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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Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2015
ISSN: 1939-2346
DOI: 10.1216/jca-2015-7-3-337