THE PROJECTIVE DIMENSION OF THE EDGE IDEAL OF A VERY WELL-COVERED GRAPH
Keyword(s):
A very well-covered graph is an unmixed graph whose covering number is half of the number of vertices. We construct an explicit minimal free resolution of the cover ideal of a Cohen–Macaulay very well-covered graph. Using this resolution, we characterize the projective dimension of the edge ideal of a very well-covered graph in terms of a pairwise$3$-disjoint set of complete bipartite subgraphs of the graph. We also show nondecreasing property of the projective dimension of symbolic powers of the edge ideal of a very well-covered graph with respect to the exponents.
2017 ◽
Vol 69
(6)
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pp. 1274-1291
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2014 ◽
Vol 22
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pp. 217-238
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2019 ◽
Vol 18
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pp. 1950118
2009 ◽
Vol 213
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pp. 360-369
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2004 ◽
Vol 56
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pp. 716-741
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1990 ◽
Vol 49
(3)
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pp. 364-385
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