Very Well-Covered Graphs via the Rees Algebra

Very Well-Covered Graphs via the Rees Algebra

A very well-covered graph is a well-covered graph without isolated vertices such that the size of its minimal vertex covers is half of the number of vertices. If G is a Cohen–Macaulay very well-covered graph, we deeply investigate some algebraic properties of the cover ideal of G via the Rees algebr...

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Veröffentlicht in:Mediterranean journal of mathematics 2024-06, Vol.21 (4), Article 135
Hauptverfasser: Crupi, Marilena, Ficarra, Antonino
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Apexes
Graph theory
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung:A very well-covered graph is a well-covered graph without isolated vertices such that the size of its minimal vertex covers is half of the number of vertices. If G is a Cohen–Macaulay very well-covered graph, we deeply investigate some algebraic properties of the cover ideal of G via the Rees algebra associated to the ideal, and especially when G is a whisker graph.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-024-02678-1