EDGE IDEALS OF WEIGHTED GRAPHS
2013 ◽
Vol 12
(05)
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pp. 1250223
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Keyword(s):
We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of "weighted vertex covers". We use these, for instance, to say when these ideals are m-unmixed. We explicitly describe which weighted cycles, suspensions, and trees are unmixed and which ones are Cohen–Macaulay, and we prove that all weighted complete graphs are Cohen–Macaulay.
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2012 ◽
Vol 49
(4)
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pp. 501-508
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2021 ◽
Vol 18
(9)
◽
pp. 4432
Keyword(s):
2019 ◽
Vol 18
(10)
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pp. 1950184
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Keyword(s):
Keyword(s):
2011 ◽
Vol 12
(01n02)
◽
pp. 109-124
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2002 ◽
Vol 39
(3-4)
◽
pp. 425-441
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1994 ◽
Vol 17
(3)
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pp. 503-510
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