Seminormality, canonical modules, and regularity of cut polytopes

Autor(en): Koley, Mitra
Romer, Tim 
Stichwörter: DECOMPOSITION; GRAPHS; IDEALS; Mathematics; Mathematics, Applied; MAX-CUT; RETRACTS; RINGS
Erscheinungsdatum: 2022
Herausgeber: ELSEVIER
Journal: JOURNAL OF PURE AND APPLIED ALGEBRA
Volumen: 226
Ausgabe: 1
Zusammenfassung: 
Motivated by a conjecture of Sturmfels and Sullivant we study normal cut polytopes. After a brief survey of known results for normal cut polytopes it is in particular observed that for simplicial and simple cut polytopes their cut algebras are normal and hence Cohen-Macaulay. Moreover, seminormality is considered. It is shown that the cut algebra of K-5 is not seminormal which implies again the known fact that it is not normal. For normal Gorenstein cut algebras and other cases of interest we determine their canonical modules. The Castelnuovo-Mumford regularity of a cut algebra is computed for various types of graphs and bounds for it are provided if normality is assumed. As an application we classify all graphs for which the cut algebra has regularity less than or equal to 4. (C) 2021 Elsevier B.V. All rights reserved.
ISSN: 00224049
DOI: 10.1016/j.jpaa.2021.106797

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