A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra

A very well-covered graph is a well-covered graph without isolated vertices such that the height of its edge ideal is half of the number of vertices. In this survey article, we gather together most of the old and new results on the edge and cover ideals of these graphs.

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Bibliographic Details
Published in:Research in the mathematical sciences 2022-06, Vol.9 (2), Article 29
Main Authors: Kimura, K., Pournaki, M. R., Seyed Fakhari, S. A., Terai, N., Yassemi, S.
Format: Article
Language:English
Subjects:
Apexes
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Developments in Commutative Algebra: In honor of Jürgen Herzog on the occasion of his 80th Birthday
Graph theory
Graphs
Mathematics
Mathematics and Statistics
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Description
Summary:A very well-covered graph is a well-covered graph without isolated vertices such that the height of its edge ideal is half of the number of vertices. In this survey article, we gather together most of the old and new results on the edge and cover ideals of these graphs.
ISSN:2522-0144
2197-9847
DOI:10.1007/s40687-022-00326-2