Combinatorial examination reveals characteristics of integral closure in n-partite graph ideals, suggesting structural insights.
Combinatorial properties of some ideals related to n-partite graphs are examined. A description of the integral closure expressed through the log set of edge ideals of complete n-partite graphs is illustrated together with the fact that edge ideals of a strong quasi-n-partite graph are not integrally closed. Moreover, we are able to determine the structure and the invariants of the integral closure of the ideals of vertex covers for the edge ideals associated to a strong quasi-n-partite graph.
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Barbiera et al. (2025) studied this question.