未混合和Cohen-Macaulay加权定向Kőnig图

Pub Date : 2019-09-29 DOI:10.1556/012.2021.58.3.1499

Yuriko Pitones, E. Reyes, R. Villarreal

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引用次数: 9

摘要

设D为一个加权有向图，其底层图为G，设I (D)为其边理想。如果G没有3、5或7环，或者G为Kőnig，我们在I (D)未混合时进行表征。如果G没有3环或5环，或者G为Kőnig，我们在I (D)为Cohen-Macaulay时进行表征。证明当且仅当当G的周长大于7或G为Kőnig且不存在4环时，I (D)是Cohen-Macaulay时，I (D)是不混合的。

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Unmixed and Cohen–Macaulay Weighted Oriented Kőnig Graphs

Let D be a weighted oriented graph, whose underlying graph is G, and let I (D) be its edge ideal. If G has no 3-, 5-, or 7-cycles, or G is Kőnig, we characterize when I (D) is unmixed. If G has no 3- or 5-cycles, or G is Kőnig, we characterize when I (D) is Cohen–Macaulay. We prove that I (D) is unmixed if and only if I (D) is Cohen–Macaulay when G has girth greater than 7 or G is Kőnig and has no 4-cycles.

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